'HE OHIO 8TATE UNIVERSITY 

August, 10^1 



THERMAL, ELECTRICAL 

AND 

MAGNETIC PROPERTIES OF ALLOYS 



BY 



ALPHEUS W. SMITH 



BULLETIN No. 20 
ENQINEEKING EXPERIMENT STATION 



PUBLISHED BY 

THE ENGINEERING EXPERIMENT STATION 

OF 

THE OHIO STATE UNIVERSITY 

COI'ITMBUS^ OHIO 



THERMAL, ELECTRICAL 

AND 

MAGNETIC PROPERTIES OF ALLOYS 



BY 

ALPHEUS W. SMITH 

PROFESSOR of PHYSICS 



PUBLISHED BY 

THE ENGINEERING EXPERIMENT STATION 

OF 

THE OHIO STATE UNIVERSITY 
COLUMBUS, OHIO 






UBRA«Y OF CONGRESS 



» 2.i-l^2,L 



THERMAL, ELECTRICAL AND MAGNETIC 
PROPERTIES OF ALLOYS.* 

BY 

ALPHEUS W. SMITH, Ph.D. 

Ohio State University. 

INTRODUCTION. 

The physical properties of alloys including hardness, con- 
ductivity for heat and electricity, thermoelectric power, magnetic 
susceptibility, rate of change of resistance with the temperature, 
etc., are intimately connected with the constitution of the alloys. 
In the absence of intermetallic compounds the physical properties 
are in general continuous functions of the composition for any 
given series of alloys. The physical property may be a linear 
function of the concentration as is ordinarily the case in conglom- 
erates or it may pass through a maximum or a minimum as in 
alloys formed of metals which are mutually soluble in each other 
in all proportions. Discontinuities may occur in cases of limited 
solubility in the solid state and the curve which represents the 
variation of the phys-ieal^rci§)e];ty..wj„th. the composition then shows 
an abrupt change iii direction at the 'concentration at which one 
metal ceases to be soluble. in the" other. In case the metals entering 
into the alloys form one or more intermetallic compounds the 
alloys will have a new 'set -of ^physi^cal p^rxDperties at the point at 
which the concentration' of The Cbrnpound-is-a maximum. 

For the purposes of this study of the relation between the 
thermal, electrical and magnetic properties of alloys and their con- 
stitution alloys may be divided into five groups. 

I. The two components are not soluble in each other and form 
no chemical compounds with each other. A metallographic study 
shows that the alloys in this case are mechanical mixtures of the 
two components. The lead-cadmium series is an example of this 
type of alloys. In such alloys the physical property is usually a 
linear function of the concentration of one of the components. 
For example, the electrical conductivity of a series of such con- 
glomerates is represented by Curve I of Fig. i. 

* Reprinted from the Journal of the Franklin Institute, July and 

August, 102 1. 

3 



Alpheus W. Smith. 



[J. F. I. 



11. The two components are soluble in each other in all propor- 
tions, i.e., they form by varying the concentration of one of the 
components an unbroken series of mixed crystals. Alloys of pal- 
ladium with silver or nickel with copper belong to this group. A 
curve representing the physical property as a function of the con- 

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90 100 



centration of one of the components is characterized by a pro- 
nounced maximum or minimum. The electrical conductivity when 
plotted as a function of the concentration of one of the com- 
ponents gives in this case a curve of the form of Curve II of 
Fig. I. 

III. Each of the components is soluble in the other to a lim- 



July, 1921.] Properties of Alloys 5 

ited extent. The alloys of this series will then consist of three 
parts, solid solutions of the first component in the second, solid 
solutions of the second component in the first and mechanical 
mixtures of saturated solutions of the first component in the 
second with saturated solutions of the second component in the 
first. A typical curve for such a property as the electrical con- 
ductivity of alloys of this group is represented in Curve III of 
Fig. I. It consists of three parts, a central portion which is linear 
where there is a mechanical mixture of one saturated solution in 
another and on either side of this a portion which is similar to the 
initial and final parts of Curve 11. 

IV. The two metals A and B form a single compound C 
(Curve IV, Fig. i) and this compound forms mechanical mixtures 
both with A and B. The curve representing the physical property 
consists of two straight lines intersecting at C. 

V. The components form one or more intermetallic compounds. 
Bismuth-tellurium alloys furnish an example of this group. In 
this case the curves, showing the physical properties as a function 
of the concentration of one of the components, may assume a 
variety of forms according to the nature of the intermetallic com- 
pound. If the compound happens to form solid solutions with 
both of the components in the alloys the curve will take the form 
of Curve V of Fig. i. In that case a compound D was formed 
which formed solid solutions with both A and B. 

PHYSICAL QUANTITIES AND UNITS. 

The specific resistance has been taken to mean the resistance 
in ohms or in microohms of a wire one centimetre in cross section 
and one centimetre in length. The electrical conductivity is under- 
stood to be the reciprocal of the specific resistance, and it has 
been expressed as the reciprocal of ohms for which the term mho 
has been used. 

The temperature coefficient of the resistance has been con- 
sidered to be the rate of change of the resistance per ohm per 
degree Centigrade. 

By the thermal conductivity is understood the quantity of heat 
in calories which will flow in one second through an area of one 
square centimetre when the temperature gradient is one degree 
Centigrade per centimetre. 



6 Alpheus W. Smith. [J- F- 1- 

The thermoelectric power has been measured against lead except 
in a few cases where it has been measured against platinum. These 
exceptions are clearly indicated on the figures. The thermoelectric 
power has been expressed as the number of microvolts for a dif- 
ference of one degree Centigrade between the junctions. For the 
rate of variation of the thermoelectric power with the temperature 
the Centigrade scale has also been used. 

The Thomson coefficient, which is a measure of the heat ab- 
sorbed or evolved in excess of the Joulean heat by a current of 
electricity flowing along an unequally heated conductor, has been 
measured in ergs. It gives the amount of heat in ergs which is 
absorbed or generated in excess of Joulean heat by a current of 
one absolute unit flowing through a conductor in which there is a 
temperature gradient of one degree Centigrade per centimetre. 

In the Hall constant which is a measure of the rotation of the 
equipotential lines under the action of a transverse magnetic field, 
the electric current, the transverse difference of potential and the 
magnetic field have been measured in absolute units and the thick- 
ness of the plate in centimetres. This constant is defined by 
the equation, 

where E = the transverse electromotive force produced by the mag- 
netic action. 

H=the intensit}- of the magnetic field. 

i = the current in the plate. 

d =^ the thickness of the plate. 
R — the Hall constant. 

For paramagnetic and diamagnetic substances the relation be- 
tween the intensity of magnetization and the magnetic field which 
produces it may be expressed by the equation, 

I = kH. 
where H = the magnetic field in gausses. 

k = the magnetic susceptibility per unit volume. 

Sometimes the magnetic susceptibility per unit mass is used. In 
such a case it is called the specific magnetic susceptibility and is 
defined by the relation, 



July, 1921.] Properties of Alloys. 

k 

where p =: density of the substitute. 



To get a measure of the elastic properties of the alloys it has 
been necessary to accept the data on these properties in a variety of 
forms. In some cases the hardness on Brinell's scale has been 
used; in others the pressure necessary to cause the metal or alloy 
to flow, and in others the tensible strength. There is no simple 
way of passing from one of these kinds of data to the other. They 
all give some measure of the cohesive forces with which the 
metals and alloys are held together, and that was all that was 
needed in this connection. 

Above the freezing point curve an attempt has been made to 
indicate the manner in which the metals mix to form the alloys 
(see Guertler, " Metallographie " ) . Where the alloys are me- 
chanical mixtures for all concentrations of the constituents, this 
fact has been indicated by placing a plus sign between the chemical 
symbols of the constituents. For example Zn + Sn means that 
tin and zinc are mechanical mixtures in all proportions. In case 
the metals A and 5 form an unbroken series of solid solutions, 
this has been indicated by writing Sol-A-B above the freezing 
point curve. If one metal ^4 is soluble to a Hmited extent in the 
other B - a saturated solid solution oi A in B has been denoted by 
/ and a saturated solid solution oi B m A by //. Where these 
saturated solid solutions then mix mechanically to form the re- 
mainder of the alloys, this fact has been indicated by / + //. For 
example in the case of the copper-silver series, the numerals above 
the freezing point curve indicated that copper dissolves about 3 per 
cent, silver, and that silver dissolves about 5 per cent, copper. 
These saturated solid solutions then mix mechanically to form the 
remainder of the alloys. 

The temperature at which the observations were made or the 
interval of temperature over which they were made has been given 
on the curves as far as possible. In a number of cases the tem- 
peratures at which the observations were made were not clearly 
given by the observer. This is especially true for observations 
made in the neighborhood of room temperature. Where the ob- 
servations were made near room temperature the letters (R.T.) 
have been written on the curves to indicate that fact. 



Alpheus W. Smith. 



[J. F. I. 



METALS INSOLUBLE IN EACH OTHER. 

Lead-Tin. 

The freezing point curve by Degens ^ (Fig. 2) for lead-tin 
alloys shows a eutectic but no evidence of compounds. Tin seems 
to be somewhat soluble in lead and possibly lead is to a small 



Fig. 2. 



Lead 



^300 



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II 



W ZO 30 40 50 60 10 80 90 100 
Weight Per Cent Tin 



degree soluble in tin. Between low and high concentrations of tin 
the alloys are heterogeneous mixtures of the crystalline phases. 

The electrical conductivities as measured by Roberts - give 
nearly a straight line as is to be expected from the fact that the 
alloys are heterogeneous mixtures of the components. The thermo- 

"^ Degens : Zeit. anorg. Chem., 63, 207, 1909. 
' Roberts : Phil. Mag. (5), 8, 57, 1879. 



July, 1921.] Properties of Alloys. 9 

electric powers have been determined by Rudolfi ^ and his results 
plotted in Fig. 2. The diamagnetic susceptibility by Honda * 
gives a curve which is nearly a straight line beginning with the 
value in lead and ending with the value in tin. In the alloys rich 
in lead (between o and 10 per cent, tin) where a solid solution 
is formed, the susceptibility decreases somewhat less rapidly than 
the linear relation requires. The linear relation between suscep- 
tibility and concentration follows at once from the fact that except 
for low and possibly high concentrations of tin the alloys are 
mechanical mixtures of the components. 

Tin-Zinc. 

The two branches of the freezing point curve (Fig. 3) by 
Heycock and Neville ^ meet at the eutectic. The changes in curva- 
ture are all gradual and there is no evidence of compounds. The 
alloys consist of heterogeneous mixtures of tin and zinc. 

Measurements of the electrical conductivity have been made 
by Matthiessen,^ Vogt/ Harris and Le Chatelier.^ More recently 
Schulze ^ has studied both the thermal and the electrical conduc- 
tivities. His observations have been plotted in Fig. 3. The 
temperature coefficient is from the work of Matthiessen and Vogt. 
Besides the observations of Rudolfi ^ on the thermoelectric heights 
there are earlier observations by RoUmann and Battelli.^^ The 
observations of Rudolfi have been used for the curve of thermo- 
elective forces. Except for minor variations these curves are 
essentially linear and typical of alloys which are formed by me- 
chanically mixing the constituents. 

Bismuth-Cadmium. 

The freezing point curve (Fig. 4) by Stoffel ^^ is composed of 
two branches meeting at the eutectic for which the temperature 

^ Rudolfi : Zeit. anorg. Chem., 67, 65, 1910. 
^ Honda : Sci. Rept. Tokio Univ., 2, 11, 1913. 

* Heycock and Neville: Jour. Chem. Soc, 71, 383, 1897. 
^Matthiessen: Pogg. Ann., no, 207, i860. 

^Vogt: Pogg. Ann., 122, 19, 1864. 

* Le Chatelier : Rev. Gen. des Sci., 6, 529^ 1895. 
® Schulze : Ann. d. Phys., 9, 555, 1902. 

" Battelli : Atti. R. Inst. Ver. (6), 5, 1886-7. 
" Stoffel : Zew. anorg. Chem., 53, 137, 1907. 



10 



Alpheus W. Smith. 



[J- F. I. 



is 148° C. In all proportions the alloys are heterogeneous mix- 
tures of bismuth and cadmium. 

The thermoelectric powers by Rudolfi "' and the magnetic sus- 
ceptibility by Gnesotto and Binghinnotto ^^ give curves which have 
the form to be expected in heterogeneous mixtures. Each of these 
curves by their steepness where the concentration of bismuth is 

Fig. 3. 




10 10 30 40 50 60 10 80 90 100 
Weight Per Cent Zinc. 



large suggests that cadmium is to a limited extent soluble in bis- 
muth. There is some evidence from the study of the homogeneity 
of these alloys that cadmium may be soluble in bismuth up to 

about I per cent. 



Rudolfi: Zcit. anorg. Chem., 67, 65. 1910. 
Gnesotto and Binghinnotto: Inst. Ven., 69, 1382. 



July, 1921.] 



Properties of Alloys. 



II 



Cadmiwn-Tin. 
The equilibrium diagram by Lorentz and Plumbridge ^* shows 
that the freezing point curve (Fig. 5) consists of two branches 
meeting at a eutectic when the alloy contains about 28 per cent, cad- 
mium. These alloys are heterogeneous mixtures in all proportions. 

Fig. 4. 

Cadmium Bismuth 



|;50 


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10 10 30 40 50 SO 10 80 90 100 
Weight Per Cent. Bismuth 

The electrical conductivity curve by Matthiessen and Vogt ^^ 
is a straight line. The curve giving the thermoelectric power as a 
function of the concentration is also a straight line. Besides these 
observations by Rudolfi ^^ there are some earlier observations by 
Battelli.^^ Both of these curves are characteristic of alloys formed 
by mechanical mixtui-es of the constituents. Concerning the other 

" Lorentz and Plumbridge : Zeit. anorg. Chem., 83, 237, 1913. 
" Matthessien : Pogg. Ann., no, 206, i860. 
''Battelli: Mevi. di Torino (2), 36, 31, 1884. 



12 



Alpheus W. Smith. 



[J. F. 1. 



thermal, electrical and magnetic properties of these alloys, no 
observations seem to be available. 

Cadmium-Zinc. 
The freezing point curve for cadmium-zinc alloys by Lorentz 
and Plumbridge ^"^ (Fig. 5 ) consists of two branches meeting at the 

Fig. 5. 




10 



line 



20 30 40 50 60 10 80 30 100 
Weight Per Cent Cadmium 

Cadmium 




10 



ZO 30 40 50 60 10 80 
Weight Per Cent Cadmium 



eutectic for which the temperature is 270° C. 
mechanical mixtures of zinc and cadmium. 

" Lorentz and Plumbridge : Zeit. anorg. Chem., 83, 236, 1913. 



The alloys are 



July, 192 1.] Properties of Alloys. 13 

The electrical conductivities at room temperature have been 
measured by Matthiessen ^^ and also by Vincentini. The curve 
showing the electrical conductivity as a function of the concentra- 
tion of one of the constituents come out to be a straight line, as it 
should for this type of alloys. Battelli ^^ has made a study of the 
thermoelectromotive forces of these alloys and a later investiga- 
tion was made by Rudolfi.^° The average values of the thermo- 
electric powers as determined by Rudolfi have been plotted on the 
curve in Fig. 5. This curve departs somewhat from a straight 
line and suggests by its minimum for low concentrations of cad- 
mium that cadmium may be soluble to a limited extent in zinc. 

Aluminium-Tin. 

The freezing point curves of Gautier ^^ and Gwyer ^" for this 
series of alloys differ by the fact that the freezing point curve of 
Gautier has a maximum corresponding to the compound AlSn 
and the curve by Gwyer shows no such maximum. The curve by 
Gwyer seems to be preferred and it has been reproduced in Fig. 6. 
According to Gwyer, there seems to be a eutectic which coincides 
nearly with the melting point of tin. Except for the possibility 
of slight solubility in each other these metals form alloys which 
are mechanical mixtures. 

Besides the observations of Broniewski ^^ on the electrical 
properties of these alloys there are available some observations by 
Pecheux on their thermoelectromotive force. The data given by 
Broniewski have been used for the curves plotted in Fig. 6. These 
curves in agreement with the freezing point curve lead to the con- 
clusion that these metals do not form definite compounds and are 
characterized by dilute solid solution of tin in aluminium and a 
mixture of this solution with tin. 

Alnminimn-Bismuth. 
Gwyer ^* found by thermal analysis that the solubility of alu- 
minium in bismuth is about 2 per cent, and that of bismuth in 

"Matthiessen: Pogg. Ann., no, 28, i860. 

"Battelli: Atti. R. Inst. Veneto (6) 5, 1148, 1886. 

^^ Rudolfi : Zeit. anorg. Chem., 67, 65, 1910. 

^^ Gautier : C. R., 123, 109, 1896. 

^^ Gwyer : Zeit. anorg. Chem., 49, 315, 1906. 

** Broniewski : Ann. de Phys. et Chem. (8) 25, 63, 1912. 

^* Gwyer : Zeit. anorg. Chem., 49, 316, 1906. 



14 



Alpheus W. Smith. 



[J. F. I. 



aluminium is about 4 per cent, at 650° C, but inappreciable at the 
melting point of bismuth. The alloys may, therefore, be regarded 
as mechanical mixtures of aluminium and bismuth. The freezing 
point curve of Fig. 7 is by Gwyer. 

Some work has been done by Pecheux ^° on the thermoelectrp- 
motive forces in these alloys. They were more fully studied by 

Fig. 6. 




10 10 30 40 50 60 10 80 90 100 
Weight Per Cent Tin 

Broniewski -^ from whose observations the curves in Fig. 7 have 
been taken. Except for a slight minimum where the concentration 
of aluminium is small the curve for electrical conductivities is 
nearly a straight line, as it should be for alloys formed by metals 
which are mechanically mixed. The curve for the temperature 

"^Pecheux: C. R., 138, 1501, 1904. 

"^ Broniewski : Ann. de Phys. et Chem. (8), 25, 66, 1912. 



July, 1921.] 



Properties of Alloys. 



15 



coefficient of the resistance has a minimum at about 95 per cent, 
bismuth. This together with the slight minimum in the electrical 
conductivity curve indicates the formation of a solid solution of 
akmiinium in bismuth. Since these minima are more pronounced 

Fig. 7. 



Bismuth 




iO 10 30 40 50 60 10 80 90 100 
V^eighi Per Cent Bismuth 

in the unannealed than in the annealed specimens the solid solu- 
tion is probably decomposed by annealing. 

METALS COMPLETELY SOLUBLE IN EACH OTHER. 

Indium-Lead. 
Lead and indium form an isomorphous mixture in all propor- 
tions. The freezing point curve (Fig. 8) by Kurnakov^ and 
Puschin -^ is a continuous curve through the melting points of 
lead and indium. 

'' Kurnakow and Puschin : Zeit. anoi-g. Chem., 52, 430, 1907. 



i6 



Alpheus W. Smith. 



[J. F. I. 



The electrical conductivity and the temperature coefficient have 
been measured by Kurnakow and Zemczuzny.^^ These authors 
have also determined the pressure necessary to cause these alloys 
to flow. All of the curves representing these physical quantities as 



Fig. 8. 



Indium 



Lead 




'0 10 iO 30 40 50 60 10 80 90 100 
Weight Per Cent Lead 



functions of the concentration are typical of alloys in which the 
constituents form a continuous series of mixed crystals. The 
pressure necessary to produce flow has a maximum value where 
the electrical conductivity and the temperature coefficient of the re- 
sistance have minimum values. This indicates that the electrical 
properties are in part at least determined by the elastic properties. 



^ Kurnakow and Zemczuzny : Zeit. anorg. Chem., 64, 149, 1909. 



July, 1 92 1.] 



Properties of Alloys. 



17 



Palladium-Silver . 

The freezing point curve of these alloys (Fig. 9) is plotted 
from the data of Ruer.^^ The metals form solid solutions in 
all proportions. 

The electrical and thermal conductivities have been determined 
by Schulze.^^ He used the same specimens which had been used 
by Giebel ^^ for the study of the electrical conductivity, the tem- 



Palladium 




10 ZO 30 40 50 60 10 80 90 100 
Weight Per Cent. Silver 

perature coefficient of the resistance, the thermoelectric heights 
and the tensile strength. All of these curves except possibly the 
one for thermoelectric heights are characteristic of metals which 

^^ Ruer : Zeit. anorg. Chem., 51, 315, 1906. 

*" Schulze : Physikal Zeitschr., 12, 1029, 191 1. 

'^Giebel: Zeit. anorg. Chem., 70, 240, 191 1. 



Alpheus W. Smith. 



[J.F.I. 



form a continuous series of mixed crystals. The elastic proper- 
ties as represented by the tensible strength of these alloys have a 
maximum where the electrical conductivity, the thermal conduc- 
tivity, the thermoelectric power and the temperature coefficient of 
the resistance have minimum values. 



Fig. 10. 



Palladium 



Gold 




30 40 50 60 10 80 90 100 
Weight Per Cent Gold 

Palladium-Gold. 

From the freezing point curve of Ruer - (Fig. lo) it is seen 
that the freezing point of these alloys changes gradually from the 
melting point of palladium to the melting point of gold. The 
metals form an unbroken series of mixed crystals. 

The electrical and thermal conductivities have been measured 
by Schulze ^ and the thermoelectric powers, the temperature coeffi- 
cient and the tensile strengths by Giebel ^" who also measured the 

^^ Giebel : Zeit. anorg. Chem., 70, 240, 1911. 



July, 1921.] 



Properties of Alloys. 



19 



electrical conductivity. All of these observations were made on 
the same specimens. These curves are all very similar to the 
corresponding curves for palladium-silver alloys and typical of 
alloys in which" there is an unbroken series of mixed crystals. 
Here as in other similar cases the elastic properties are related to 
the electrical and thermal properties. 

Palladium-Platinum. 
The freezing point curve for this series of alloys does not seem 
to have been studied. The physical properties (Fig. 11) clearly 

Fig. II. 

Palladium Platinum 




10 



30 40 50 60 10 SO SO 100 
Weight Per Cent. Platinum 

indicate that these metals mix in all proportions forming a con- 
tinuous series of mixed crystals. 

The thermal and electrical conductivities which have been given 
in Fig. 1 1 have been taken from the work of Schulze who made 



2G 



Alpheus W. Smith. 



[J. F. I. 



his observations on the same specimens on which Giebel ^" had 
made observations on the electrical conductivity, the temperature 
coefficient of the resistance, the thermoelectric power and the ten- 
sile strength. There is an evident parallelism between the elec- 



FlG. 



Gold 



Silver 




10 



10 30 "10 50 SO 10 80 SO 100 

Weight Per Cent Silver 



trical and thermal conductivities. In this series as in the palladium- 
silver series the curve of tensile strengths has a maximum where 
the electrical and thermal conductivities have minimum values. 

Gold-Silver. 

Roberts-Austen and Kirke Rose, confirming the work of Hey- 

cock and Neville,^^ showed that gold and silver solidify in the form 

of an unbroken series of mixed crystals. The freezing point 

changes continuously from its value in gold to its value in silver. 

''Heycock and Neville: Phil. Trans. A., 189, A, 69, 1897. 



July, 1 92 1.] Properties of Alloys. 21 

The curve for the electrical conductivities (Fig. 12) is plotted 
from the observations of Matthiessen.^* The average thermo- 
electric power has been calculated from the data of Rudolfi ^^ and 
the Hall constant from the work of Beckman.^^ The hardness 
has been measured by Kurnakow.^'^ The similarity between the 
four lower curves in Fig. 12 is very evident. The elastic property 
has a maximum value where the other properties have mini- 
mum values, indicating that the elastic forces in the alloys help to de- 
termine the Hall effect as well as the electrical conductivity, the tem- 
perature coefficient of the resistance and the thermoelectric powers. 

Copper-Gold. 

From the observations of Kurnakow and Zemczuzny ^* on the 
freezing points of copper-gold alloys (Fig. 13) it is found that 
the freezing point curve runs in a simple way from the melting 
point of copper to the melting point of gold. It has a minimum 
where the alloy contains about 25 per cent, copper. These metals 
form a continuous series of solid solutions. 

The electrical conductivity of this series has been studied by 
Matthiessen "^ and in later times by Kurnakow, Zemczuzny and 
Zasedatelev *° f tom whose observations have been taken both the 
curve for electrical conductivities and the curve for temperature 
coefficient of resistance. The hardness which has been measured 
by Kurnakow and Zemczuzny *^ shows the maximum which is 
characteristic of a series of solid solutions. The average thermo- 
electric power as found by Rudolfi ^ has been used for the ther- 
moelectric height curve. Except for the two peaks in the curve 
for the electrical conductivity and two corresponding peaks in the 
curve for the temperature coefficient of the resistance, this set of 
curves is very similar to the set found for alloys of platinum and 
palladium in which there was a continuous series of solid solutions. 

^* Matthiessen : Pogg. Ann., no, 190, 1861. 

^' Rudolfi : Zeit. anorg. Chem., 67, 65, 1910. 

^^ Beckman : Com. fr. Phys. Lab. Univ. of Leiden, 130, 27, 1912. 

" Kurnakow : Zeit. anorg. Chem., 60, i, 1908. 

^* Kurnakow and Zemczuzny: Zeit. anorg. Chem., 54, 163, 1907. 

^^ Matthiessen : Pogg. Ann., no, 217, i860. 

^"Kurnakow, Zemczuzny and Zasedatelev: /. Inst, of Metals, 15, 305, 1916. 

^^ Kurnakow and Zemczuzny: Zeit. anorg. Chem., 60, i, 1908. 



22 



Alpheus W. Smith. 



[J. F. I. 



Potassium-Rubidium. 

These metals form isomorphous mixtures in all proportions. 
The freezing point curve has not been located and it seems to 
be unknown. 

The observations on the electrical conductivity and on the rate 
of change of the resistance with the temperature (Fig. 14) are 

Fig. 13. 




10 10 30 40 50 60 10 80 30 100 
Weight Per Cent Gold 



due to Kurnakow and Nikitinsky."*- They also determined the 
pressures required to cause the alloys to flow. The electrical con- 
ductivity as a function of the concentration of one of the com- 
ponents is represented by a continuous curve with a very slight 
mininrum. This is characteristic of isomorphous mixtures. With 
rising temperature the minimum is displaced toward rubidium — 

''Kurnakow and Nikitinsky : Zcit. anorg. Cheiu., 88, 151, 1914. 



July, 1921.] 



Properties of Alloys. 



23 



the metal with the least conductivity. The curve for the rate of 
change of the resistance with the temperature shows the minimum 
characteristic of this type of alloys. The only difference between 
these curves and those obtained under similar conditions for most 
isomorphous mixtures is the smaller decrease in the electrical con- 
ductivity which is produced by adding rubidium to potassium. In 
most cases in which solid solutions are formed this decrease is 

Fig. 14. 




2: 


15 





/4 






>< 


n 


^ 




i. 


\i 






>1 


w 


c 




^ 


10 


^ 


9 



10 20 5Q ^0 50 60 10 80 90 IGO 
Weight Per Cent. Rubidium 

much larger than it is in this case. The elastic properties as 
measured by the pressure necessary to cause the alloys to flow 
show the characteristic maximum found in isomorphous mixtures. 

Platinum-Iridiiim . 
The equilibrium diagram for this series has not been located. 
These metals probably form solid solutions. 



24 



Alpheus W. Smith. 



[J. F. I. 



The electrical conductivity, the temperature coefficient, the 
thermoelectric power, and the tensile strength have been studied 
by Giebel ^^ for this series of alloys for concentrations of iridium 
between o and 35 per cent. These curves are reproduced in 
Fig. 15. The tensile strength is a linear function of the concen- 



FlG. 1 = 



Platinum 



Iridi 




5 10 15 20 25 

Weight Per Cent. Iridium 



tration of iridium over this interval. The thermoelectric power 
passes through a maximum between 15 and 20 per cent, iridium. 
The addition of iridium to platinum lowers both the electrical 
conductivity and the temperature coefficient in the way to be ex- 
pected on the assumption that the metals form solid solutions. 



Giebel: Zeit. anorg. Chem., 70, 247, 1911. 



July, 1 92 1.] 



Properties of Alloys. 



25 



Copper-Nickel. 

. The freezing point curve for this series of alloys (Fig. 16) is 
the one worked out by Guertler and Tammann.^'* These metals 
form an unbroken series of solid solutions. 

The electrical conductivity and the temperature coefficient have 



Fig. 16. 



Nickel 




10 10 30 40 50 60 10 80 30 100 
Weight Per Cent Nickel 



been measured by Feussner.*^ The curves thus obtained are char- 
acteristic of a continuous series of solid solutions. The thermo- 
electric power by Englisch *^ and the hardness by Kurnakow and 
Papke *^ also give the type of curve to be expected in alloys which 

*^ Guertler and Tammann : Zeit. anorg. Chem., 53, 281, 1907. 
^Feussner: Verhand. d. physik Gesel. zu Berlin, 10, 109, 1891. 
" Englisch : Phys. Consts. Soc. Fran, de Phys., p. 654, 1893. 
*'' Kurnakow and Papke : Zeit. anorg. Chem., 87, 274, 1914. 



26 Alpheus W. Smith. [J. F. I.. 

are solid solutions. The curve of hardness shows a maximum 
where the curve for the electrical conductivity has a minimum, 
thus showing that the elastic properties in a measure determine 
the electrical conductivity and its variation with the temperature. 
The curve for the magnetic susceptibilities has been taken from the 
observations of Gans and Fouseca.*^ The Hall constant is by 
the author."^^ Neither the Hall constants nor the magnetic sus- 
ceptibilities seem to depend on the concentration in the way to be 
expected for solid solutions. 

Iron-Nickel. 

The freezing point curve (Fig. 17) by Guertler and Tam- 
mann °° indicates that iron and nickel form a continuous series of 
solid solutions. On the freezing point curve as sometimes given 
there seems to be a change in curvature at the concentration cor- 
responding to the compound NiaFe, from which this compound is 
sometimes inferred. 

The specific heat, the electrical conductivity, the temperature 
coefficient, the thermal conductivity and the thermoelectric heights 
have been measured by Ingersoll and others. ^^ The flux densities 
given in Fig. 17 are from the observations of Yensen '"' and were 
measured for an external magnetic field of 400 gausses. The 
specific heat is a maximum at the concentration of the possible 
compound NisFe. The electrical conductivity, the temperature 
coefficient and the thermoelectric power have minimum values 
where the intermetallic compound might be formed. Of all these 
curves only the one for the thermal conductivities has the general 
form to be expected in a series of alloys which are an unbroken 
series of solid solutions. The complexity of the curves in this case is 
doubtless due to the fact that both nickel and iron are polymorphic. 

Magnesium-Cadmium. 

The freezing point curve by Grube ^^ has a point of inflection 
VA^here the concentration corresponds to the compound MgCd. 

*^ Gans and Fouseca : Ann. d. Phys., 61, 742, 1920. 

*^ Smith: Phys. Rev., X. S., 17, 24, 1921. 

^ Guertler and Tammann : Zeit. anorg. Chein., 45, 205, 1905. 

" Ingersoll : Phys. Rev., N. S., 16, 85. 1920. 

®^ Yensen : Jour. A. I. E. E., 396, 1920. 

^" Grube : Zeit. anorg. Chem., 49, 72, 1906. 



July, 1921.] 



Properties of Alloys. 



27 



This change in curvature is not very evident in the curve as plotted 
in Fig. 18. According to this equiUbrium diagram the alloys are 
solid solutions of two crystalline phases. About the equilibrium 
in this series there is still considerable doubt. 

The electrical conductivity, the temperature coefficient, and 



Nickel 




10 10 30 'JO 50 60 10 80 90 100 
Weight Per Cent. Nickel 



hardness have been measured by Ourazow.''^ On both of these 
curves the compound MgCd is clearly marked by a cusp. This 
compound is also indicated on the curve for hardness. On either 
side of the compound there is a second cusp in the curve for 
electrical conductivity and for the temperature coefficient. If 
these cusps were absent the curves would have the normal course 

^' Ourazow : Zeit. anorg. Cliem., 73, 31, 1912. 



28 



Alpheus W. Smith. 



[J. F. 1 



to be expected on the assumption that alloys to the right of the 
compound are solid solutions of cadmium and the compound 
MgCd and those to the left of the compound solid solutions of 
magnesium with the compound MgCd. The thermal analysis is 



Magnesium 




10 10 30 40 50 60 10 80 30 100 
Weight Per Cent Cadmium 



not in agreement with the indications given by the thermal and 
electrical properties in this case. 



METALS WITH LIMITED SOLUBILITY IN EACH OTHER. 

A lu minium- Zinc . 
The freezing point curve of aluminium-zinc alloys from 
Gautier ^^ (Fig. 19) is made up of two branches which meet at 
the temperature of fusion of the eutectic. There are no compounds 

^Gautier: Bull. Soc. Encour. (5), i, 1293, 1896. 



July, 1 92 1.] 



Properties of Alloys. 



29 



and Shepherd ^^ concludes from a micrographic study that alumi- 
nium-zinc alloys are formed of two solid solutions and a mechani- 
cal mixture of these solid solutions. 

Besides the observations of Broniewski " on the electrical 



Fig. 19. 




10 ZO 30 ^0 50 60 10 80 90 100 
Weight Per Cent Zinc 



properties of these alloys there are earlier observations by Battelli ^^ 
and Pecheux.^'^ The curves in Fig. 19 have been plotted from 
the observations of Broniewski. The curves all belong to that 
group of alloys which are formed from metals which are soluble 
in each other to a limited extent and in which the solid solutions 

"^Shepherd: Jour. Phys. Chem., 9, 504, 1905. 
"Broniewski: Ann. de Chem. et Phys. (8), 25, i, 1912. 
^'Battelli: Atti. R. Inst. Veneto. (6), 5, 1148, 1886-7. 
*" Pecheux: C. R., 138, 1103, 1904. 



30 



Alpheus W. Smith. 



[T. F. 1. 



thus formed mix with each other mechanically. The central por- 
tions of the curves are nearly linear as should be the case for 
mechanical mixtures. 

Copper-Silver. 
A thermal analysis of copper-silver alloys has been made by 
Heycock and XeviUe.-- Their results have been confirmed by the 

Fig. 20. 




10 20 30 40 50 60 10 80 90 IOC 
Weight Per Cent Silver 



work of Friedrick and Leroux and Lepowiski.^'" from whose work 
the freezing point curve (Fig. 20) is taken. Copper forms a 
solid solution with silver and silver with copper until the con- 
centration of the copper in one case and silver in the other is about 

*- Heycock and Neville: Phil. Trans. A., 189, 25. 1S97. 
^ Lepowiski : Zeit. anorg. Chem., 59, 289. 1908. 



July, 1921.] Properties of Alloys. 31 

5 per cent. The remainder of the alloys are heterogeneous mix- 
tures of these saturated solid solutions. 

The hardness, the electrical conductivity and the temperature 
coefficient of this series are due to Kurnakow, Puschin and Sem- 
kowsky.^" Where a solid solution is formed between copper and 
silver there is a marked lowering of both the electrical conduc- 
tivity and the temperature coefficient. Hence for high as well as 
low concentrations of silver these curves are very steep. The 
central portions of these curves, although somewhat irregular, ap- 
proach the form to be expected in a region where there is a me- 
chanical mixture of two crystalline phases. There is a marked 
increase in hardness over the intervals in which solid solutions are 
formed. The remainder of the hardness curve is such as is to be 
found where the alloys are mechanical mixtures of two crystal- 
line phases. Except for some irregularities this set of curves 
clearly belongs to metals which form solid solutions with each 
other to a limited extent and then these solid solutions mix me- 
chanically to form the remainder of the alloys. 

Bismiitli-Lead. 

The freezing point curve by Kapp and Charpy ^^ (Fig. 21) 
has a eutectic at 56.5 per cent, bismuth. Herold ^^ finds that for 
suitable concentrations lead and bismuth form mixed crystals, but 
the region over which these solid solutions extend is not clearly 
defined. The solutions, however, are rather dilute. The remainder 
of the alloys are mechanical mixtures of two crystalline phases. 

The hardness curve indicates by the increase in hardness for 
low and high concentrations of bismuth the formation of solid 
solutions at the beginning and end of this series. The remainder 
of the curve of hardness over the region where the alloys are 
heterogeneous mixtures is a straight line. The thermal and elec- 
trical conductivities by Schulze ^^ have minima for alloys con- 
taining 4 or 5 per cent, of lead. This as well as the initial drops 
in these curves for alloys containing from o to 15 per cent, bis- 
muth is further evidence for the formation of solid solutions at 
either end of this series. The thermoelectromotive force which 

*^ Kurnakow, Puschin and Semkowsky: /. d. riiss. phys. Che))!., 42, 7;^;}, 1910. 
"Barlow: Zeit. anorg. Chem., 70, 183, 1911. 
"Herold: Zeit. anorg. Chem., 112, 131, 1920. 
^'Schulze: Ann. d. Phys., 9, 564, 1902. 



32 



Alpheus W. Smith. 



[J.F.I. 



has been studied by Battelli ®^ shows a rapid decrease for the 
addition of small quantities of lead to bismuth. The character- 
istics of this curve in this region are similar to the characteristics 
of the other curves over this same region. 



Fig. 2] 



Lead 



Bismuth 




i) \0 20 30 40 50 60 10 80 30 
Weight Per Cent. Bismuth 



Antimony -Tin. 

The freezing point curve by Williams " (Fig. 22) consists of 
three parts. Later study of equilibrium in this system has been 
made by Konstantinow and Smirnow, LeGris and Loebe. Be- 
tween 90 and 100 per cent, antimony there is a solid solution of 
tin in antimony and between o and 10 per cent, tin there is a 

'"Battelli: Atti. R. Inst. Veneto (6), 5, 1148, 1886. 
"'Williams: Zcit. anorg. Cheui., 55, 12. 1907. 



July, 1921. 



Properties of Alloys. 



33 



solid solution of antimony in tin. When the metals are present in 
equal concentrations a new crystalline phase is formed, probably 
the intermetallic compound SnSb. Those alloys which are not 
solid solutions for large and small concentrations of antimony are 
mechanical mixtures of two crystalline phases. 

The electrical conductivity and the temperature coefficient are 




^ 2 



l-^^ 



Antimony 



35 ^ 



25^ 

20 ' 
5 I 

G 



Temperature Coef of Resist. _ 
(25-100°) 




4 I 


-Si 



10 20 30 % 50 60 10 80 90 100 

Weight Per Cent. Antimony 



by Konstantinow and Smirnow ^^ and the magnetic susceptibility 
by Leroux.^^ The initial decrease in the electrical conductivity, 
the temperature coefficient of the resistance and the thermoelectric 
power "^ caused by the addition of tin to antimony give evidence 

"' " Annual Tables of Constants and Numerical Data," Vol. 2, p. 345. 

^'Leroux: C. R., 156, 1764, 1913. 

''° Hutchins : Jour. Am., Amer. Jour. Sci., 48, p. 226, 1894. 



• 34 Alpheus W. Smith. [J- F. l. 

of the formation of a solid solution over this region. On the 
other side of the "diagram where the concentration of antimony is 
less than lo per cent, the curve for the electrical conductivity and 
for the temperature coefficient show again the presence of solid 
solutions. The curve for the magnetic susceptibilities indicates 
the compound by a change in its curvature at that concentration. 
The evidence for the structure of this series is not conclusive. 

Lead-Thalliitin. 

The freezing point curve for lead-thallium alloys has a very 
flat maximum between 30 and 40 per cent. lead. This was re- 
garded by Lewkonja '^ as evidence of the compound PbTh,. 
Kurnakow and Puschin '" found that this maximum is displaced 
by the addition of tin to the alloys. If the maximum were due to 
a true compound, this displacement should not occur. Hence the 
existence of the compound is in doubt. Thallium forms a solid 
solution with lead until the concentration of thallium is about 75 
per cent., and lead dissolves in thallium until the concentration of 
lead is about 4 or 5 per cent. Rejecting the evidence for the exist- 
ence of the compound, the alloys between 5 and 25 per cent, lead 
are heterogeneous mixtures of a saturated solution of lead in thal- 
lium with a saturated solution of thallium in lead. 

The electrical conductivity and the mean temperature coefficient 
as determined by Kurnakow and Schemtschuschny ~'^ have been 
plotted in Fig. 23. There is a minimum in both curves. This 
minimum is in the region over which lead and thallium form an 
isomorphous mixture. The addition of lead to thallium causes a 
decrease in the electrical conductivity and also in the temperature 
coefficient of the resistance. This decrease is followed by an in- 
crease which extends to the concentration at which the solution is 
saturated with lead. Between 5 and 25 per cent, lead there is a 
straight line portion in the curve. This is over the region where 
the alloys are mechanical mixtures of two cr\'stalline phases. The 
pressure required to produce flow in these alloys is taken from 
these same observers. The curve thus obtained shows the char- 
acteristic relation between the electrical and the elastic properties. 

" Lewkonja : Zeit. anorg. Chem., S'2; 452, 1907. 

'" Kurnakow and Puschin : Zeit. anorg. Chem., 52. 430. 1907. 

'^Kurnakow and Schemtschuschny: Zeit. anorg. Cheui., 64, 156, 1909. 



July, 1 921.1 



Properties of Alloys. 



35 



Lead-Anthnony. 
The freezing point curve (Fig. 24) by Gontermann ' ^ shows a 
eutectic in the neighborhood of 13 per cent, antimony. Gonter- 
mann finds some evidence of an intermediate crystalline constitu- 
ent. Aside from this possible exception these alloys may be 
considered mechanical mixtures. 



Tha 


Hium 




Fig 

PbTU 


■ 23 








Lead 




l|/;MI 


V- 


t 

1 






E 




1 




|375 

■pZ5 
1^300 






























1 


k 














/ 


^ 


1 






'>Cf 


^ 










V 




1 








^ 






/' 






1 
1 
1 






















1 
























! 
1 








! 
i 




2; 

Q CO 

20 5 1 

10 S|, 

qj Q 

ct^ 

4 5 
3 ^ 










1 








1 






"K 






i 


pressure 


^ife: 






r 




-^ 


r\ 


! 




i 


^ 










1 
















>?* 






j 
















Y\ 


\ 




i 








5 


/y 


5; 




\ 


'^ 


'^p'Coefloff^^^-^ 


^ 




5 6 


1 
1 




'Hi 

1 


) — 


- 










l_r&. 






1 














/ !~i: 


^ 3 


V 


N 


X. 


1 
1 
1 




j 


V 


/ 








\ 


'i 


Cor 


1 


P- 






i 


1 












U 1 P 


Ml' 




' \ 


/( 


) I 


3 
Wei 


4 


5 

Per 


6 

Ce, 


1 1 
It L 


1 8 
eaa 


9 


1 10 






The curve for electrical conductivities is by Matthiessen ; ^^ for 
the thermoelectric powers by Rudolfi ; ^^ for magnetic susceptibili- 
ties by Leroux,'' and for the electromotive force of dissolution 
by Pouchine. The curve for the thermoelectric powers is a straight 



'* Gontermann : Zeit. anorg. Chem., 55, 419, 1907, 
^^Matthiessen: Pogg. Ann., no, 28, i860. 
''' Rudolfi : Zcit. anorg. Chem., 67, 65, 1910. 
"Leroux: C. R., 156, 1764, I9i3- 



36 



Alpheus W. Smith. 



[J. F. I. 



line until the alloy contains 90 jDer cent, antimony. At that con- 
centration the thermoelectric power rises rapidly to its value in 
pure antimony. At about this same concentration the curve for the 
magnetic susceptibilities and for the electromotive forces of solu- 
tion show peculiarities. There seems to be nothing in the struc- 



FlG 




10 10 30 m 50 60 10 80 30 100 
Weight Per Cent Antimony 



ture of the alloys to offer an explanation of this sudden change in 
the direction of the curves at this concentration. 

Copper-Cobalt. 
The equilibrium diagram by Sahmen '^ from which the freez- 
ing point curve (Fig. 25) is taken shows that copper and cobah 
form mixed crystals with each ether over a limited region. Cop- 

'^ Sahmen : Zcit. anova Chem., 57, 1908. 



July, 1921.] 



Properties of Alloys. 



37 



per is soluble in cobalt up to 8 per cent, and cobalt in copper up to 
5 per cent, cobalt. The remainder of the alloys are a heterogene- 
ous mixture of a saturated solution of cobalt in copper and a 
saturated solution of copper in cobalt. 

The curve for electrical conductivity, temperature coefficient 
and thermoelectric height are from the observations of Reichardt."^^ 



Fig. 25. 



Cobalt 




?^ 


■^ 




^~ 




>!h 




<^ 


15 


>< 




>i 


10 







^ 


5 


^ 



10 ZO 30 40 50 60 10 80 90 100 
V^eighi Per Cent Cobalt 



Each of these curves shows a discontinuity since alloys with less 
than 60 per cent, copper were so brittle that they could not be 
forged into wires and were investigated in the form of castings. 
Aside from these discontinuities the curve for electrical conduc- 
tivity and the curve for temperature coefficient of resistance are 
typical of alloys in which the constituents are soluble in each other 



Reichardt : Ann. d. Phys., 6, 842, 1901. 



38 



Alpheus W. Smith. 



[J. F. 1. 



to a limited extent. The central portion of the curves are essen- 
tially linear, as they should be for alloys formed by the mixture 
of two crystalline phases. The curve for thermoelectric powers 
is peculiar in view of the fact that the addition of cobalt to copper 
causes a rapid decrease in the thermoelectric height and the addi- 
tion of copper to cobalt causes a somewhat less rapid increase in 
the thermoelectric height of cobalt. 



Fig. 26. 



mony 




^ 10 10 30 10 50 60 10 80 30 

Weight Per Cent Antimony 



Bismuth- Antimony . 

The freezing point curve (Fig. 26) by Huttner and Tam- 

mann ^° shows that the freezing points of these alloys decrease 

gradually from the melting point of bismuth. Concerning the 

structure of the alloys there seems to be some doubt. Between 18 

^ Huttner and Tammann : Zeit. anorg. Chem., 44, 131, 1905. 



July, 1921.] Properties of Alloys. 39 

and 100 per cent, antimony they may be considered solid solu- 
tions of bismuth and antimony and between o and 18 per cent, 
antimony they are mixtures of bismuth and a saturated solution 
of antimony and bismuth. 

The thermoelectromotive forces of this series have been studied 
by Seebeck, Rollmann, Matthiessen, Becquerel, Sundell, BattelU, 
Hutchins and more recently by Haken ^^ from whose data the curve 
of Fig. 26 is taken. The electrical conductivity is known from the 
work of Matthiessen, Calvert and Johnason and Haken. ^^ The 
magnetic susceptibility by Honda and Sone ^^ is a linear function 
of the concentration until the alloy contains about 90 per cent, 
antimony where the proportionality fails. The curve for the 
thermal conductivities by Gehlhoff and Neumaier ^^ is very similar 
to the curve for electrical conductivities by Haken, This shows 
that Wiedmann and Franz's law holds approximately for these 
alloys. The curve for the temperature coefficient is characteristic 
of alloys which are soHd solutions. The Hall constant ^* is evi- 
dently closely related to the thermoelectric power in agreement 
with the suggestion of Beattie that there is a proportionality be- 
tween these two quantities. 

Bismuth-Tin. 

The freezing point curve (Fig. 27) from data of Stoffel ^^ and 
Lepkowski ^^ consists of two branches meeting at a eutectic. Ex- 
cept for small and possibly large concentrations of tin where the 
metals may be soluble in each other to a limited extent, these 
alloys are mechanical mixtures of bismuth and tin. 

The thermoelectric powers of these alloys have been studied 
by Hutchins ^'^ and also by Caswell. ^^ The curve for the Thomson 

*^ Haken: Ann. d. Phys., 32, 291, 1910. 

*^ Honda and Sone: Sci. Repts. Univ. Tokio, 2, 5, 1913. 

*' Gehlhoff and Neumaier : Verh. d. Deutsch. Phys. Ges., p. 876, 1913. 

** Smith: Phys. Rev., 32, 178, 1911. 

'^ Stoffel : Zeit. anorg. Cheni., 53, 148, 1907. 

^^ Lepkowski : Zeit. anorg. Chem., 59, 287, 1908. 

*^ Hutchins : Amer. Jour. Sci., 48, 226, 1894. 

'* Caswell : Phys. Rev., N. S., 12, 226, 1918. 



40 



Alpheus W. Smith. 



[T. F. I. 



effect as determined by Laws and also by Caswell is very similar 
to the curve for the thermoelectric heights. Each curve shows a 
pronounced maximum when a small quantity of tin is present in 
the alloy. The curves for electrical and thermal conductivities by 
Schulze ^^ have minima where the preceding curves have maxima. 



Fig. 2- 



Bismuth 



^^300 



■^150 



g/50 




10 ZO 30 40 50 60 10 80 30 100 
Weight Per Cent. Bismuth 

These maxima and minima occur in the region in which the alloys 
seem to be dilute solid solutions of tin in bismuth. The remainder 
of the curve for thermal conductivity as well as the curve for 
electrical conductivity is roughly linear, the form to be expected in 
alloys which are heterogeneous mixtures. The curve for mag- 
netic susceptibilities has been contributed by Gnesotto and Binghin- 



Schulze : Ann. d. Phys., g, 566, 1902. 



Aug., 1921.] Properties of Alloys. 41 

notto.^'^ The addition of tin to bismuth rapidly decreases the 
diamagnetic susceptibility in the interval where the preceding 
curves showed either maxima or minima, that is, in the interval of 
possible solid solutions. The remainder of the curve suggests 
mechanical mixtures except for the irregularities where the alloys 
are nearly all tin. 

Copper-Zinc. 

The freezing point curve (Fig. 28) is by Shepherd and others.®^ 
The structure of this series is complex. Copper dissolves zinc 
until the concentration of zinc is about 35 per cent, and zinc dis- 
solves copper until the concentration of copper is 2 or 3 per cent. 
The intermediate alloys may be considered heterogeneous mix- 
tures of two crystalline phases. 

The electrical conductivity, the temperature coefficient, the ther- 
moelectric powers and the rate of change of thermoelectric power 
have been measured by Norsa.^^ Between o and about 35 per cent, 
zinc these curves have the form characteristic of alloys which are 
solid solutions. The remainder of the curves seem too complicated 
to admit of analysis in terms of the structure of the alloys. The 
thermal conductivity is known from the work of Calvert and 
Johnson. ^^ The course of this curve is somewhat irregular. The 
curve for the magnetic susceptibility has been plotted from data by 
Weber.^^ Between o and 35 per cent, zinc it is a straight line. 

Copper-Tin. 

The structure of this series of alloys is complex. The freez- 
ing point curve (Fig. 29) by Heycock and Neville '''^ gives evi- 
dence of one compound CusSn. Tin is soluble in copper until 

''" Gnesotto and Binghinnotto : Inst. Ven., 6g, 1382. 

'■*' Guertler : Metallographie, i, 459. 

"' Norsa : C. R., 155, 348, 1912. 

"^ Calvert and Johnson: Phil. Mag., 18, 354, 1850. 

"^ Weber : Ann. d. Phys., 62, 666, 1920. 

"^Heycock and Neville: Phil. Trans. A., 202, i, 1904. 



42 



Alpheus W. Smith. 



[J.F.I. 



there is about 13 per cent, copper present. The remainder of the 
alloys may be considered as mechanical mixtures of two 
crystalline phases. 

The curve for hardness by Kurnakow and Zemczuzny ®® con- 
sists of two straight lines and a curve of gentle slope. The two 

Fig. 28. 

line 
'^^ 'I + TI (Complex)' -*WE 2 

■ ■ i — I I \iooo^ 




10 10 30 40 50 60 10 80 30 100 
Weight Per Cent Zinc 

straight lines intersect where the concentration of tin is about 1 1 
per cent, and thus mark the concentration at which tin ceases to be 
soluble in copper. The intersection of the second straight line 
with the third portion of the curve marks the concentration for the 
compound CusSn, The curves for the electrical conductivity, the 
temperature coefficient, the thermoelectric power and its variation 



Kurnakow and Zemczuzny : Zeit, anorg. Chem., 60^ 9, 1908. 



Aug., 1 92 1.] 



Properties of Alloys. 



43 



with the temperature have been plotted from the observations of 
Leroux.^^ Between o and 35 per cent, tin the curves for electrical 
conductivities and that for the temperature coefficients are typi- 
cal of alloys which are solid solutions. Where the solution be- 
comes saturated the direction of the curves suddenly changes. The 
position of the intermetallic compound is marked on these curves 



Fig. 29. 



Cu.S 




\Q ZQ ZO 40 50 60 10 80 30 100 
Weight Per Cent. Tin 

by cusps. The curve for thermal conductivities is very similar to 
the curve for electrical conductivities. Wiedemann and Franz's 
law must, therefore, hold approximately for these alloys. The 
curve for the magnetic susceptibilities by Clifford ^^ does not show 

"Leroux: C. R., 155, 35, 1912. 

^^ Clifford: Phys. Rev., 26, 424, 1908. 



44 



Alpheus W. Smith. 



[J.F.J. 



the compound, but this is probably due to the fact that the points 
on the curve near the compound are too far apart. 




Siher-Tiu. 

The freezing point curve for silver-tin alloys (Fig. 30) by 
Petrenko ^^ is in complete agreement with the curve obtained by 
Heycock and Neville. Silver is only slightly soluble in tin and 
tin is soluble in silver until the concentration of tin is about 18 
per cent. The other alloys are, therefore, heterogeneous mixtures 
of two crystalline phases. 

The electrical conductivity curve by Matthiessen ^°° shows an 
initial rapid drop for alloys rich in silver. This is characteristic of 

^''Petrenko: Zcif. anorg. Chem., 50, 138, 1906; also 53, 200, 1907. 

'"' Matthiessen : Pogg. Ann., no, 215, i860. 



Aug., 1921.] ' Properties of Alloys. 45 

alloys which are solid solutions. The remainder of the curve has 
the general shape of curves for a mechanical mixture of two 
crystalline phases. 

Siher-Bismiifh. 

Petrenko ^°^ has also given the freezing point curve for silver- 
bismuth alloys (Fig. 30). It shows a eutectic for alloys contain- 
ing 2.5 per cent, silver. Under suitable conditions bismuth is 
somewhat soluble in silver. Most of the alloys are heterogeneous 
mixtures of a saturated solid solution of bismuth in silver 
and of bismuth. 

The form of the electrical conductivity curve by Matthiessen ^°^ 
suggests the formation of solid solutions of bismuth in silver fol- 
lowed by a region in which the alloys are heterogeneous mix- 
tures. The electrical conductivity curve for this series is very 
similar to the curve for silver-tin alloys. Some observations on 
thermoelectromotive forces have been made by Battelli.^"^ 

Lead-Cadmiiim. 

The freezing point curve, according to StoffeP°* (Fig. 31), 
consists of two branches meeting at a eutectic for which the tem- 
perature is 249° C. Lead and cadmium form a solid solution 
until the concentration of cadmium is about 5 per cent., at which 
concentration the solution is saturated. The remainder of the 
alloys are a mechanical mixture of this saturated solution 
and cadmium. 

The electrical conductivity by Matthiessen ^°- is nearly a linear 
function of the concentration. There are no points on the curve 
in the region between 95 and 100 per cent, lead in which the solid 
solutions are now known to be formed. 

Lead-Silver. 

The freezing point curve by Petrenko ^°^ (Fig. 31) shows a 
eutectic for which the temperature is 303.9° C. Lead is soluble in 

"^ Petrenko : Zeit. anorg. Chem., 50, 138, 1906 ; also 53, 200, 1907. 
"^Matthiessen: Pogg. Ann., no, 208, i860. 
"'Battelli: Atti. R. Inst. Ven. (6), 5, 1148, 1886. 
"* Stoffel : Zeit. anorg. Chem., 53, 152, 1907. 



46 



Alpheus W. Smith. 



[J.F.I. 



silver until the alloy contains about 5 per cent. lead. The re- 
mainder of the allovs are heterogieneous mixtures of this solid 



Fig. 31. 




10 30 ^G 50 60 70 SQ 90 100 
Weight Per Cent. Silver 

solution and lead. The structure of these alloys is very similar to 
the structure of the lead-cadmium alloys. 

The curve for electrical conductivities by ^latthiessen ^^' is 
very steep between 100 and 97 per cent, silver. This is the region 

^'^ Matthiessen: Fogg. Ann., no. 212, i860. 



Aug., 1 92 1.] 



Properties of Alloys. 



47 



in which a soHd solution of lead in silver is formed. For alloys 
containing less than 50 per cent, silver the curve becomes nearly a 
straight line, which is characteristic of mechanical mixtures of 
two crystalline phases. 

Fig. 32. 

Tellurium Te5n Tin 



!^600 




10 ZO 30 40 50 60 70 80 90 100 
Wei^lit Per Cent. Tin 



METALS FORMING COMPOUNDS WITH EACH OTHER. 

Tellitriiim-Tin. 

The freezing point curve (Fig. 32) by Fay ^"^^ gives the inter- 
metallic compound TeSn, with a eutectic on either side. The 
results of Kobayashi ^°' are in agreement with those of Fay. 
Alloys containing less than 48 per cent, tin are mechanical mix- 
tures of tellurium; the compound TeSn and those containing 

^•^ Fay : Joxw. Ainer. Chem. Soc, 29, 1265, 1907. 
"'Kobayashi: Zeit. anorg. Chem., 69, i, 1911. 



48 Alpheus W. Smith. [J-F.l. 

more than 48 per cent, tin are mechanical mixtures of tin and the 
compound TeSn. 

The thermoelectric powers and the electrical conductivities in 
Fig. 32 are by Haken ^°^ and the magnetic susceptibilities from 
the work of Honda and Sone.^°^ The compound is indicated on 
each of the curves. The curve for magnetic susceptibilities con- 
sists of two straight lines which intersect at the concentration giv- 
ing the compound TeSn. One of these straight lines corresponds 
to mixtures of tellurium and TeSn and the other to mixtures of 
tin and TeSn. Between 55 and 100 per cent, tin the thermo- 
electric power curve is a straight line of small slope. 

Bisiuuth-Telluriuin. 

The freezing point curve of this system (Fig. 33) by Monke- 
meyer ^^^ indicates the compound BioTcg with a eutectic on either 
side. Alloys to the left of the compound are mixtures of Bi and 
BioTes and those to the right are mixtures of Te and the 
compound BioTcg. 

The thermoelectric power and the electrical conductivity are 
taken from the observations of Haken/^^ the Hall constant at 
room temperature from Trabacci ^^- and the magnetic suscepti- 
bility from the work of Honda and Sone.^^^ The presence of the 
compound is clearly marked on each of the curves. The curve for 
the Hall constant is very similar to the curve for the thermo- 
electric powers. A proportionality between the Hall constants and 
the thermoelectric powers has been recognized by Beattie and 
these curves are in agreement with the suggestion. Beside the 
work of Honda and Sone on the diamagnetic susceptibility of 
these alloys there is some earlier work by ]\Iendenhall and Lent ^^^ 
who failed to find in their curve an indication of the compound. 
Honda and Sone point out that this was probably due to the fact 

"* Haken: Aiui. d. Phys., 32, 291, 1910. 

^"' Honda and Sone : Sci. Repts. Imp. Univ. Tokio, 2, 10, 1913, 

"'' Monkemeyer : Zeit. anorg. Chem., 46, 415, 1905. 

"'Haken: Ann. d. Phys., 32, 291, 1910. 

"'Trabacci: Nuovo Cim., 9, 95, 1915. 

"^ Honda and Sone : Sci. Repts. Imp. Univ. Tokio, 2, 12, 1913. 

"^Mendenhall and Lent: Phys. Rev., 32, 406, 1911. 



Aug., 1921.] 



Properties of Alloys. 



49 



that Mendenhall and Lent did not take the points in the neigh- 
borhood of the compound close enough together. Between i and 
41 per cent, telluritim and between 60 and 100 per cent, tellurium 
the susceptibility curve is nearly a straight hne which is character- 
istic of mechanical mixtures. 



Bismuth 




10 10 30 40 50 60 10 80 90 IOC 
Weight Per Cent. Tellurium 

Bisjjnith-Magiiesiinu. 

The freezing point curve (Fig. 34) by Grube ^^^ gives one 
compound BioAIgs and one eutectic for this combination of metals. 
Another eutectic is probably formed between bismuth and the 
compound BisMgs, but the temperature of this eutectic nearly 
coincides with the melting point of bismuth. Alloys to the left 
of the compound consist of heterogeneous mixtures of bismuth 

"" Grube : Zeit. anorg. Chem., 49, 85, 1906. 



50 



Alpheus W. Smith. 



[J. F. I. 



and the compound BisMga and those to the right of mixtures of 
magnesium with the compound Bio^Igs- 

The electrical conductivity and the average temperature coeffi- 
cient have been determined by Stepanow.^^^ Neither of these 
curves show the presence of the compound BisIMgs. This may 
be due to the fact that the points in the neighborhood of this 

Fig. 34. 



Bismuth 


Bi. 


Mgs 












Magnesium 




BuMqsl 


- 


Mg.-f-BizMg 




i ^ 
1 








1 
1 














1 




7f;n 






















-1 650 




/r 


N, 










Pn\r 


i 




/ 


1 
1 


\ 




_J 


!iS- 


~ingjj^ 




^jjO 


/ 


r 














1 




/ 


I 


■ 




* 










^ 


^ 




1 


















5.0^ 
4.5 i 
4.0 1 
3.5 1 


^ CDU 




I 














,n( 


^0) 




\ 


r 


i 








r ^ 








•> 


^ TemperatureJ^ 


ei^.^^-^^ 


1 20 


' 1 


• ■■ 






,./ 














.f 


z' 








I 








(< 


,^ 








j 


' i ,c 


V 










1 10 

1 ^ 


i j 


1 .V 












1 i 


^A 


f 














1 


y 
















! 


/ 




















-<ii 












1 





10 iO 50 40 50 60 10 80 30 100 
Weight Per Cent. Magnesium 

compound were not taken sufficiently close together. The course 
of the curves on either side of the compound somewhat resembles 
straight lines, indicating that the alloys on the two sides of the 
compound are mechanical mixtures. 

Magnesiuin-Tin. 
The equilibrium diagram for magnesium and tin shows one 



Stepanow : Zeit. anorg. Chcm., 78, i, 1912. 



Aug., 1921. 



Properties of Alloys. 



51 



intermetallic compound, MgoSn. There is a eutectic on either side 
of this compound. The freezing point curve of Fig. 35 is by 
Grube/^^ Magnesium does not seem to be soluble in tin, but 
Grube finds that magnesium dissolves about 6 per cent, of tin. 
With the exception of alloys in this region, the alloys of this series 
are mechanical mixtures of two crystalline phases. 




10 10 30 40 50 60 10 80 90 100 
Weight Per Cent. Magnesium 

The electrical conductivities and the temperature coefficients of 
the resistance are known from the work of Stepanow.^^*^ The 
addition of tin to magnesium causes a rapid drop in the electrical 
conductivity and the temperature coefficient. The steepness of 
these curves for large concentrations of magnesium confirms the 
existence of solid solutions of magnesium and tin where the con- 
centration of tin is small. The compound is marked by a rapid 

"■ Grube : Zeit. anorg. Chem., 46, 1905. 



52 



Alpheus W. Smith. 



fJ.F.I. 



drop in the temperature coefficient and a minimum in the electrical 
conductivity. Between o and about 28 per cent, and between 40 
and 65 per cent, magnesium the temperature coefficient is nearly- 
constant. This constancy could be inferred from the fact that the 
alloys over these regions are mechanical mixtures, in the former 
case of tin and the compound SnMgo and in the latter case of the 



Fig. 36. 



line fig Iriz 



Magnesium 




compound SnAI< 
and tin. 



/O m 30 iO 50 60 10 80 90 100 
l/^eight Per Cent. Magnesium 

and a saturated solid solution of magnesium 



M agnesium-Zinc . 

These two metals, according to Grube,^^^ from whose work 
the freezing point curve of Fig. 36 is taken, form one inter- 
metallic compound with the formula MgZn2. On either side of 

"^ Grube : Zeit. anorg. Chem., 49, 80, 1906. 



Aug.. 1921.] Properties of Alloys. 53 

this compound is a eutectic and the alloys to the left of the com- 
pound may be regarded as heterogeneous mixtures of zinc and the 
compound MgZns and those to the right of the compound, mixtures 
of magnesium and the compound MgZus. It seems possible that 
zinc may form dilute solid solutions with magnesium. 

The electrical conductivities and the temperature coefficients 
of the resistance are from the observations of Stepanow/^^ These 
curves are similar in form to the corresponding curves for mag- 
nesium-tin alloys. In the region where the concentration of zinc 
is small and dilute solid solutions of zinc in magnesium may be 
formed both of these curves are steep, especially the curve of 
electrical conductivities. The position of the compound is marked 
by a rapid decrease in both the temperature coefficient and the 
electrical conductivity. 

Bis rnuth- Thallium . 

The freezing point curve by Chickashige ^^^ (Fig- 37) indi- 
cates a compound at the concentration corresponding to BisTlg 
with a eutectic on either side of it. The freezing point curve 
seems to have three maxima, but only one of them corresponds 
to a simple atomic ratio, and that is the one giving the compound 
BisTls. A micrographic examination also locates a compound in 
this neighborhood. 

The electrical conductivity curve for these alloys are by Whit- 
ford ^^^ and the magnetic susceptibilities by Mendenhall and 
Lent.^^^ Both the electrical conductivity and the magnetic sus- 
ceptibility were measured at room temperature. The presence 
of the intermetallic compound is clearly indicated on. both of 
these curves. 

A lu minium-Magnesium . 

Grube ^-^ whose freezing point curve is reproduced in Fig. 38 
finds one maximum which corresponds to either ALMgs or AlgMgi. 
These compounds lie so close together that it is difficult to choose 
between them, but Grube concludes that AlsMg^ is the more prob- 

"" Stepanow : Zeit. anorg. Chem., 78, 25, 1912. 
"" Chickashige : Zeit. anorg. Chem., 51, 328, 1906. 
^'' Whitford : Phys. Rev., 35, 144, 1912. 
"^ Mendenhall and Lent: Phys. Rev., 32, 415, 1911. 
'■'' Grube : Zeit. anorg. Chem., 45, 225, 1905. 



54 



Alpheus \\\ Smith. 



[J. F. I. 



able. To the right of this compound the alloys may be considered 
mechanical mixtures of Mg and the compound Al3Mg4 and for 
lower concentrations of magnesium they are mechanical mixtures 
of aluminium and the compound Al3Mg4. 

Besides the observations of Broniewski ^^* from which the 



Fig. 37. 



Thallium 
1 




10 10 30 40 50 60 10 80 90 100 
Weight Per Cent. Bismuth 

curves in Fig. 38 have been plotted there are observations by 
Pecheux ^^° on the thermoelectromotive forces of some members 
of this series. According to the interpretation of Broniewski, two 
compounds are indicated by his curves : viz., AlMg and AlsMgs. 
Of these compounds AL^Igs is much more clearly marked than 
the compound AlMg. 

^^ Broniewski : Ann. de Phys. et Chem. (8), 25, 76, 1912. 
"^ Pecheux : C. R., 139, 1202, 1904. 



Aug., 1921.] 



Properties of Alloys. 



55 



Copper- Arsenic. 

The freezing point curve of Fig. 39 is by Friedrich.^^^ From 
the equiUbrium diagram and from a metallographic study of these 
alloys it is found that copper and arsenic form two compounds 
CusAs and CusAsa and that arsenic dissolves in copper up to 4 
per cent. 

Fig. 38. 

Aluminum AliMg^ Magnesium 




0. W 10 30 40 50 60 10 80 90 100 

Weight Per Cent. Magnesium 

Some observations on the electrical conductivity of copper- 
arsenic alloys have been made by Matthiessen and Holtzmann ^^^ 
and later by Hampe.^"^ Friedrich also gives some data on the 
electrical resistance of these alloys for low concentrations of 
arsenic. The specific resistance of these alloys and the tempera- 

'"^ Friedrich : Metallurgie, 5, 529, 1908. 

'"Matthiessen and Holtzmann: Pogg. Ann., no, 229, i86c. 

'^' Hampe : Chemiker, Ztg., 726, 1892. 



56 



Alpheus W. Smith. 



[J. F. I. 



ture coefficient (Fig. 39) are the values given by Puschin and 
Dischler.^^^ The electrical resistance of copper is much increased 
by the addition of small quantities of arsenic, and the temperature 
coefficient is decreased. This occurs in the region where a solid 
solution of arsenic in copper is formed and is characteristic of the 
formation of such solutions. When the concentration of arsenic 
is about 28.5 per cent, the specific resistance has its maximum 



Copper 








Fig. 39. 

Cu^As 




Arsenic 




■*- ! Cu -1- CusAs 


'< 


' ?' -'^ 




^1100 

fiooo 

"^900 
c 

^800 
^ 700 


*^ 












\t' ■ 








1 
1 














>v ■^ 


% 






! 
















\ 


0.- 




1 


















\ 


/ 


' 1 

1 


V. 


X 






60 










V 






\ 


'^ 






1 














/ 


/ 


1 

1 




\ 






50 








/ 


/ 




1 
















/ 
















4/1 E 








'§^ 






1 










V 






/^ 
















30 f 


-0 ^ 


/ 


/ -S? 








1 
1 










^^' 








1 










20 I 

ctz 


or 3 


/ 










! 










/ 








r,'^ 


>\ 


fo-iooj- 








"^ 


A 








w 


1 . 


/ 






,»vV 


1 
















c/ 


/ 


1 



















./ 


/ 




1 










1 ' 


V 




/ 






1 















S 


^ 








! 












) t 


IL 


) \ 
Veiq 


1 I 

ht / 


I 


5 3 

'ent. 


3 

Ars 


5 4 

?nic 


i 


5 5 






value. This maximum value comes at the concentration for the 
compound CusAs. The temperature coefficient decreases from its 
value in pure copper, passes through a minimum for 6 per cent, 
arsenic and then increases until the concentration corresponding to 
the compound CusAs is reached. Beyond this concentration the 
temperature coefficient remains nearly constant. 

^^'' Puschin and Dischler : Zeit. anorg. Chcm., 80, 65, 1913. 



Aug., 1921.] 



Properties of Alloys. 



57 



L ead-Magnesium. 
The freezing point curve ^^° (Fig. 40) shows a maximum cor- 
responding to the compound MggPb with a eutectic on either side. 
For concentrations of magnesium less than that corresponding to 
the compound the alloys are heterogeneous mixtures of lead and 

Fig. 40. 

Lead PbMg2 Magnesiu m 




10 ZO 30 40 50 60 10 80 90 
Weight Per Cent Magnesium 

MgsPb and for greater concentrations they are mixtures of the 
compound MggPb and magnesium. 

The curve for electrical conductivities by Stepanow ^^^ 
(Fig. 40) shows that the electrical conductivity decreases rapidly 
with the addition of lead to magnesium until the alloy contains 
about 5 per cent. lead. At the concentration corresponding to the 
compound MgsPb the electrical conductivity passes through 
a minimum. 

"" Grube : Zeit. anorg. Chem., 44, 117, 1905. 
"^ Stepanow : Zeit. anorg. Chem., 78, 12, 1912. 



58 Alpheus W. Smith. [J.F.I. 

Magnesium-Copper. 

The freezing point curve (Fig. 40) as determined by 
Urasow ^^^ and also Sahem ^^^ shows two maxima corresponding 
to the intermetalHc compounds CusMg and CuMga. There are, 
therefore, in the equihbrium four types of crystalhne substances 
to be considered : Cu, CuoMg, CuMgs and Mg. None of these 
substances seems able to form solid solutions with any of the 
others. The alloys then become divided into three groups, mix- 
tures of Cu with CugMg; mixtures of CusMg with CuMga and 
mixtures of Mg and CuMga. 

The electrical conductivity has been measured by Stepanow.^^* 
He also gives data from which the temperature coefficient can be 
calculated. These data are, however, very irregular and have not 
been plotted. Between 100 and 45 per cent, magnesium the curve is 
nearly a straight line, as it should be for a mechanical mixture of 
Mg and CuAIgo. Between 43 and 20 per cent, magnesium it is 
again a straight line corresponding to the mixture of CuMgs and 
CusMg. The early part of the curve for small concentrations of 
magnesium is steep and suggests a solid solution rather than a 
mechanical mixture. 

Antimony-T eUliriiim . 

The freezing point curve of this series by Fay and Ashley ^^^ 
(Fig. 41) gives a maximum corresponding to the compound 
SbaTca. There is also a eutectic for which the temperature is 
421° C. The compound forms a continuous series of mixed 
crystals with antimony but does not mix in the same way with 
pure tellurium. 

The electrical conductivity and the thermoelectric power for 
this series have been measured by Haken.^^^ The addition of 
tellurium to antimony causes a rapid decrease in both the electrical 
conductivity and the thermoelectric power. Both of these quan- 
tities pass through a minimum and rise rapidly to their value for 
the compound SboTcs. The course of these curves between o and 
60 per cent, tellurium is typical of alloys formed of two crystalline 

"^Urasow: Jour. niss. Chem. Ges., 39, 1566, 1909. 
*^ Sahem : Zeit. anorg. Chem., 57, 3, 1908. 
^^Stepanow: Zeit. anorg. Chem., 78, 20, 1912. 
^^Fay and Ashley: Amer. Chem. Jour., 27, 1902. 
"' Haken : Ann. d. Phys., 32, 291, 19 10. 



Aug., 1921. 



Properties of Alloys. 



59 



phases, forming solid solutions. The compound is clearly marked 
on both curves. The magnetic susceptibility of these alloys has been 
studied by Honda/^'^ Between 100 and 62 per cent, tellurium the 
curve is nearly a straight line. Over this region the susceptibility 
varies little. The compound is marked by a sudden change in the 
direction of the curve at the concentration of the compound. 



Antimony 



Tellurium 




10 10 30 40 50 60 10 80 3D 100 
Weight Per Cent. Tellurium 

Antimony- Aluniininm. 

The freezing point curve (Fig. 42) by Gautier ^^^ has two 
maxima. One corresponds to the compound AlSb, but the exist- 
ence of a second compound is questioned. 

The diamagnetic susceptibility of these alloys has been con- 

"^ Honda: Sci. Rept. Imp. Univ. Tokio, 2, 9, 1913. 

"* Gautier : " Contribution a I'etude des alleages," 112, 1901. 



6o 



Alpheus W. Smith. 



[J.F.I. 



tributed by Honda. ^^^ The curve showing the susceptibility as a 
function of the concentration is made up of two straight hnes 
which intersect where the alloy contains 18.4 per cent, aluminium, 
i.e., at the concentration for the compound AlSb. The character 
of the susceptibility curve indicates that alloys containing less 
than 18.4 per cent, aluminium are mechanical mixtures of anti- 



FiG. 42. 



Anti mony /ll5b 



Aluminum 



5b+ I— ^ AISb + AI 
'='S^S£/pg Points 




Weight Per Cent. Aluminum 

10 10 30 iO 50 6.0 10 80 30 



Antimony 



5b Mr. 



Mane 




1200 
IIOO 




1000 
300 


eg 


800 
100 


N 


600 





10 10 30 "10 50 60 10 80 dO 100 
Weight Per Cent. Manganese 

mony and the compound AlSb, and those containing more than 

18.4 per cent, aluminium are mixtures of aluminium and the 

compound AlSb. 

Anfiinony-Manganese. 

The compound SbMns is indicated on the freezing point curve 

(Fig. 42) by Williams. ^^^ Between lOO and about 52 per cent. 

"'Honda: Sci. Rept. Imp. Univ. Tokio, 2, 9, 1913. 
""Williams: Zeit. anorg. Cheiiu, 55, i, 1907. 



Aug., 1921.] Properties of Alloys. 61 

manganese the alloys are heterogeneous mixtures of Mn and the 
compound SbMn,; between o and about 31 per cent, manganese 
they are a mixture of antimony and a secondary crystalline phase. 
The thermal and electrical properties of these alloys have not 
been studied. The magnetic susceptibility at 550° C. has been de- 
termined by Honda. ^^^ His observations were made with a field 
of 10.9 kilogausses. The susceptibility for this temperature is 
nearly independent of the temperature. From o to 31.2 per cent, 
manganese the susceptibility is nearly a linear function of the 
concentration. In this region the alloys are mechanical mixtures 
of Sb and SbMns. Between 31.2 and 40.7 per cent, manganese 
the character of the susceptibility curve changes because a new crys- 
talline phase appears. Between 40.7 and 47.8 per cent. Mn there 
is another straight line portion, followed by another linear portion 
from 50.5 to 100 per cent. Mn, the region over which the 
alloys are heterogeneous mixtures of manganese and a second 
crystalline phase. 

Aiitinwny-Zinc. 

The freezing point curve for this series as determined by 
Monkmeyer ^^^ (Fig. 43) has two maxima, one corresponding to 
the compound SbZn and the other to the compound SbsZug. The 
alloys divide themselves into three groups — heterogeneous mix- 
tures of Zn and SbsZus, mixtures of SbsZuo and SbZn and mixtures 
of SbZn and Sb. The structure of the series of alloys is very 
similar to the structure of the antimony-cadmium series. 

The curve for the magnetic susceptibilities by Honda ^^'^ con- 
sists essentially of two straight lines intersecting at the concen- 
tration for the compound SbZn. Over the region where there is 
supposed to be a mixture of SbsZua and SbZn the curve departs 
somewhat from a straight line. The linear relation between the 
susceptibility and the concentration confirms the existence of the 
mechanical mixtures indicated by thermal analysis. The curves 
for the specific resistance, the thermoelectric power and the Hall 
constant ^^^ show clearly the compound SbZn, but they give no evi- 
dence of the compound Sh^Zuo. 

"' ]\Ionkmeyer : Zcit. anorg. Cheiii., 43, 182, 1905. 
"^ Honda : Sci. Rept. Imp. Univ. Tokio, 2, 6, 1913. 
^ " Smith : Phys. Rev., 32, 178, 191 1. 



62 



Alpheus W. Smith. 



[J. F. I. 



Antiiiiony-Cadiuium. 

The freezing point curve (Fig. 44) by Treitschke '^^ gives a 

compound SbCd which is stable and another SboCds which is 

probably unstable. Between o and about 40 per cent, antimony 

the alloys are mixtures of Cd and Sb.Cdo : between 40 and ^2 per 



Antimony 



Fig. 43- 
ZnSb In^Sbj 




10 ZO 50 i^ 5u 6C n 
Weight Per Cent. Zinc 

cent, mixtures of SbCd and SbsCdg and between -^2 and 100 per 
cent, mixtures of SbCd and Sb. 

The curves for the specitic resistance, temperature coefficient 
and thermal conductivitv are from the observations of Eucken 
and Gehlhoff.^*^ 

The thermoelectric power of this series has been frequently 
studied. The curve of ther moelectric powers in Fig. 44 is from 

^** Treitschke : Zeit. anorg. Chem., 50, 217, 1906. 

^"^ Eucken and Gehlhoff : Verh. d. dent. Phys. Ges., 169, 1912. 



Aug., 1921.] 



Properties of Alloys. 



63 



Haken.^*^ The Hall constant is by the author.'^' The position of 
the compound is very evident on all of these curves except the 
curve for the thermal conductivities. On either side of this com- 
pound and at some distance from the concentration at which it 
appears neither the resistance, nor the thermoelectric power, nor 



Cad mi 



Fig. 44. 



Antimony 




\0 10 30 40 50 60 ID 80 30 100 
l^ eight Per Cent. Antimony 

the Hall constant changes rapidly with a change in the composi- 
tion of the alloys. 

Magnesium-Silver. 

The freezing point curve ^*^ ( Fig. 45 ) gives one maximum at 
the concentration for the compound MgAg. There is probably a 
second compound MggAg. Between o and 8.5 per cent, magnesium 

"" Haken : Ann. d. Phys., 32, 291, 1910. 

"^ Smith : Phys. Rev., 32, 178, 1911. 

"^ Zemczuzny : Zeit. anorg. Chem., 49, 403, 1906. 



64 



x\lpheus W. Smith. 



[J. F. I. 



there is a solid solution of magnesium in silver followed by a 
mechanical mixture of this solid solution and the compound MgAg. 
There then follows a regiqn in which there is a mixture of MgsAg 
and MgAg. Between o and 60 per cent, silver the alloys are 
mixtures of Mg and MgaAg. 

Fig. 45. 
Ma gnesium MgsAg hq^q Silv er 




10 10 dO 40 50 60 10 m 90 100 
Weight Per Cent 5/li/er 

The curve for the hardness ^^^ of these alloys shows these 
regions quite clearly. It is made up of four straight lines. One 
of these lines extends from o to 60 per cent, silver, over the region 
in which the alloys are mechanical mixtures of Mg and MggAg; 
the next from 60 to 82 per cent, silver where there is a mixture of 
MgAg and MggAg; the third one from 82 to 91 per cent, silver 
where there is a mixture of MgAg and a saturated solid solution 
of magnesium in silver; the last from 91 to 100 per cent, silver, 
the region of the solid solutions of magnesium in silver. The 

"^Desch: " Intermetallic Compounds," p. 15. 



Aug., 1921.] 



Properties of Alloys. 



6s 



curves for the electrical conductivity and the temperature coefficient 
are by Smirnow and Kurnakow/^° The positions of both com- 
pounds are marked on these curves. The initial rapid decrease in 
the electrical conductivity and the temperature coefficient for fairly 



Fig. 46. 



5iU 

1000 
^ 900 
^ 800 

N 600 

^■500 

400 



Ag35b 



Antimony 



' L44t^' "^^^^'^ ■ Ti^i 




'% '^ 

^ IZ 
X 10 

I ' 

"^ 10 10 30 iO 50 60 10 80 30 
Weight Per Cent. Antimony 

small concentrati-ons of magnesium in silver is in agreement with 
the conception that solid solutions are formed over this interval. 
The nearly linear course of these curves between 10 and 58 per 
cent, silver follows from the fact that the alloys are mechanical 
mixtures of two crystalline phases over this interval. 

Silver -A ntim ny . 
Petrenko ^^^ gives the freezing point curve (Fig. 46). By a 
sudden change in curvature it suggests the compound AgsSb. A 
^^ Smirnow and Kurnakow : Zeit. anorg. Cheni., 72, 31, 1911. 
"^ Petrenko : Zeit. anorg. Chein., 50, 1906. 



66 Alpheus W. Smith. [J-F. I. 

solid solution of silver in antimony is formed until the concentra- 
tion of the silver becomes about 4 per cent, and a solid solution of 
antimony in silver until the concentration of antimony is about 10 
per cent. Between about 10 and 28 per cent, antimony there is a 
mechanical mixture of AgsSb and a saturated solid solution of 
antimony in silver and between 28 and 96 per cent, a mixture of 
AgsSb and a saturated solution of silver in antimony. 

The curve for the thermoelectric heights as well as that for the 
electrical conductivities has been worked out by Haken,^^^ and 
these curves are reproduced in Fig. 46. The compound is clearly 
indicated and the region in which silver is soluble in antimony is 
marked by the steepness of both curves in this region.' In like 
manner the interval in which antimony is soluble in silver is indi- 
cated by the characteristic drop in the electrical conductivity. The 
decrease in the thermoelectric power for small concentrations of 
antimony is less marked. 

Aluuiin'mni-C p per . 

By thermal analysis Gwyer ^^^ finds evidence of three com- 
pounds : AloCu, AlCu and AlCus (Fig. 47 ) . The compound ALCu 
is decomposed before fusion. Between o and 9 per cent, copper 
there are solid solutions of aluminium in copper, followed by a 
region of mixed crystals of CU3AI and CuAl; a second region of 
mixtures of CuAl and CuAL, and a third region of mixtures of 
CuAlo and a saturated solution of copper in aluminium. 

A number of observations have been made on the electrical 
properties of these alloys. Among the earlier observations in this 
region are those made by LeChatelier/^* Dewar and Flemming/^^ 
Battelli/^^ Steinmann,^^'^ Pouchine ^^^ and Pecheux.^^^ The curves 
in Fig. 47 have been plotted from the data given by Broniewski.^®° 
On the curve for electrical conductivity and also on the one for 
the temperature coefficient the three compounds are indicated by a 

"^Haken : Ann. d. Phys., 32, 291, 1910. 

^^^ Gw3^er : Zeif. anorg. Chem., 57, 113, 1908. 

'^ LeChatelier : C. R., loi, 454, 1890. 

^^ Dewar and Flemming: Phil. Mag. (5), 36, 271, 1893. 

'''Battelli: Atti. R. Inst. Veneti. (6), 5, 1148, 1886-7. 

^^ Steinmann : C. R., 130, 1300, 1900. 

"^ Pouchine : Jour. Soc. phys. Chem. russ., 39, 528, 1907. 

^''Pecheux: C. R., 148, 1041, 1909. 

"^^ Broniewski : Ann. de Phys. et Chem. (8), 25, 91, 1912. 



Aug., 1921.1 



Properties of Alloys. 



67 



change in the slope of the curves at the concentrations correspond- 
ing to the compounds. On the curve for the thermoelectric power 
and also on the curve for the variations of the thermoelectric 
power with the temperature the compounds AlgCu and AlCus are 
marked by minima in the curves. Over the region between 91 and 
100 per cent, copper where solid solutions of aluminium in copper 

Fig. 47. 

Aluminum CuAk CuAl CujAI Cop per 




ZQ 30 40 50 60 10 80 90 100 
Weight Per Cent. Copper 

are formed the electrical conductivity and the temperature coeffi- 
cient show the decreases characteristic of such solutions. 

A luminium-Silver. 

The freezing point curve (Fig. 48) by Petrenko ^*^^ gives two 
compounds, AlAga and AlAgs. These compounds are indicated by 
a change in the curvature of the freezing point curve at the concen- 
tration at which the compound occurs. This change in curvature is 

"^ Petrenko : Zeit. anorg. Chem., 46, 49, 1905. 



68 



Alpheus W. Smith. 



[J. F. I. 



not very evident from the curve as plotted in Fig. 48. Between o 
and 87.5 per cent, silver the alloys are mechanical mixtures of alu- 
minium and the compound AlAgs ; between 87.5 and 91.5 per cent, 
silver mixed crystals of AlAgz and AlAgs ; between 91.5 and 94 per 
cent, silver mixtures of AlAgs and saturated solid solutions of 

Fig. 48. 



Aluminum 



Silver 




10 



20 30 40 50 60 10 80 90 100 
Vl/eiaht Per Cent. Silver 



aluminium in silver, and between 94 and 100 per cent, silver solid 
solutions of aluminium in silver. 

The curves for the electrical conductivity, temperature coeffi- 
cient, thermoelectric power and variations of the thermoelectric 
power with the temperature have been taken from the observa- 
tions of Broniewski.^*^" The compound AlAgs is marked clearly 
by a peak in each of the curves except the curve for the electrical 
conductivity where the peak is small. On the other hand, a 

"^ Broniewski : Ann. de Phys. et Chem. (8), 25, 83, 1912. 



Aug., 1921.] 



Properties of Alloys. 



69 



minimum occurs in each of the curves except the curve for elec- 
trical conductivities where the concentration corresponds to the 
compound AlAgg. Except for the two peaks in the curve for the 
temperature coefficient that curve as well as the curve for elec- 
trical conductivities has the form which is found in binary alloys 

Fig. 49. 
Aluminum NiAlj Ml, NiAl Nickel 



Al +NiAk 




10 20 30 40 50 60 10 SO SO 100 
Weight Per Cent Nickel 

of metals which form limited solid solutions with each other and 
then these solid solutions mix mechanically to form the remainder 
of the alloys of the series. 

A luminiiim-Nickd. 

The freezing point curve (Fig. 49) by Gwyer ^^^ gives a maxi- 
mum near the concentration corresponding to the compound NiAl. 
Between o and 42 per cent, nickel the alloys are mixtures of Al 



Gwyer : Zeit. anorg. Chem., 57, 133, ic 



/O Alpheus W. Smith. [J.F.I. 

and NiAla ; between 42 and 52 per cent, nickel mixtures of NiAlg 
and NiAla; between 52 and 68 per cent, nickel mixtures of NiAU 
and NiAl, and between 68 and 100 per cent, nickel an unsaturated 
solution of aluminium in nickel. 

The electrical conductivity, the temperature coefficient, the 
thermoelectric power and its variation with the temperature have 
been plotted from the observations of Broniewski.^^^ In the inter- 
val between 45 and 84 per cent, nickel there are no observations on 
account of the brittleness of the alloys in this region. The com- 
pound NiAls is indicated by a peak on the temperature coefficient 
curve. The magnetic susceptibilities by Honda ^^^ have been meas- 
ured at 25° C. for alloys containing less than 80 per cent, nickel. 
For alloys containing more than 80 per cent, nickel the suscepti- 
bilities were determined at 550° C. A magnetic field of from 5 
to 12 kilogausses was used. Until the alloys contain 80 per cent, 
nickel the susceptibility curve consists of four straight lines inter- 
secting at the concentrations at which a new crystalline 
phase appears. 

Nickel-Tin. 

The composition of this series of alloys is very complex. The 
freezing point curve by Gautier ^^^ has been reproduced in Fig. 50. 
Five different kinds of crystals are present in the solidified alloys. 

No observations have been found on the thermal and electrical 
properties of these alloys. The magnetic properties have been 
studied by Honda. ^^^ On the alloys containing less than 60 per 
cent, nickel the observations were made at 25° C. On the re- 
mainder of the alloys the observations were made at 550° C. — a 
temperature above the transformation "point. The external mag- 
netic field was from 5 to 12 kilogausses. The ferro-magnetic prop- 
erties disappear when the concentrations of the constituents 
correspond to the compound NigSn. So long as the alloys are 
composed of the same two kinds of crystals in varying concentra- 
tions the susceptibiHty is a linear function of the concentration. 
Where one type of crystal disappears and is replaced by another 
the slope of the curv^e suddenly changes. 

"* Broniewski : Ann. de Chem. et Phys. (8), 25, 108, 1912. 
"^ Honda: Ann. d. Phys., 32, 1015, 1910. 
"' Gautier : C. R., 122, 109. 



Aug., 1 92 1. J 



Properties of alloys. 



71 



Iron-Vanadium. 
The composition of iron and vanadium alloys has been studied 
by Vogel and Tammann,^" and it has been found that they solidify 
in the form of an unbroken series of mixed crystals. The freez- 
ing point curve (Fig. 50) has a minimum in the neighborhood of 
35 per cent, vanadium. 



Fig. 50. 



Iron 



Vanadium 



1700 




1600^ 
1500 I 
1600.^ 



80 90 100 
Nickel 



1500 
1300 



30 


Q 


WOO 


c 




>< 


900 


Q^ 











10 


^0 


100 


N 









^ 




W) 


500 











Ll- 


\0 




300 





10 10 30 40 50 60 10 80 30 100 
Weight Per Cent Nickel 

The electrical and thermal properties of this series of alloys do 
not seem to have been studied. There are observations by 
Honda ^^^ on the intensity of magnetization. These observations 
were made at 16° C. and with a magnetic field of 9.9 gausses. The 
intensity of magnetization of iron decreases slowly with an in- 
creasing concentration of vanadium until that concentration is 

^" Vogel and Tammann : Zeit. anorg. Chem., 58, 79, 1908. 
'"* Honda : Ann. d. Phys., 32, 1910, 1912. 



J2 



Adpheus W. Smith. 



[J.F.L 



reached at which the freezing point curve has its minimum. Here 
there is an extraordinarily rapid decrease in the intensity of mag- 
netization so that an alloy containing more than 40 per cent, of 
vanadium is very feebly magnetic. 

Fig. 51. 



Copper 



Antimony 



1100 



1000 



<o 



^900 
^ 800 
•§ 700 
it 600 



500 



, 


14 


<^ 








^ 


I? 


^ 




.^ 


in 


Ij 




■^ 




r 


8 


^ 




<.i 


6 


<!i 








LU 


4 



^^ 


'u + C 


"UsSi 




? 




CuS 




^, J 


1 


"^ 


b + 


5b 




\ 






1 
1 

1 














\ 


s. 




'1 

1 
















\ 




1 
1 


1 












\ 


1 
1 


















\ 


-i 




X^ 


V 


9 Pc 


. \ 








1 

! 






S^//7 


\o<-' 


-"^ 








1 
1 
1 




















1 
1 
1 




















1 
1 




A 
















1 
1 
1 


/ 


1 


he 


. 






V 






1 
1 
1 


/ 




■s. 


h 


h 


^: 




^ 

^^^ 




1 
1 

1 


/ 














1 

L 


r 













10 20 30 40 50 60 10 80 
WeJt^ht Per Cent. Antimony 



90 100 



Copper- Antimony. 

Baikow ^^^ has given a complete equilibrium diagram from 
which the freezing point curve (Fig. 51) is taken. The compound 
CusSb is formed. Alloys to the right or left of this compound 
are heterogeneous mixtures of two crystalline phases. Copper, 
according to Stead, dissolves about 0.3 per cent, antimony. 

For small concentrations of antimony the electrical conduc- 
tivity curve by Matthiessen ^'° is ver}- steep. This is in the region 

^''^ Baikow : Jour, reiss. Phys. Chem. Ges., 36, iii, 1904. 
^'"Matthiessen: Pogg. Ann., no, iQO, i860. 



Aug., 1921.] Properties of Alloys. 73 

where antimony and copper form dilute solid solutions. The 
electrical conductivity curve shows a sudden change in direction 
where the concentrations correspond to the compound CusSb. 
Between 55 and 100 per cent, antimony the conductivity curve is 
a straight line. Over this interval the alloys are mechanical mix- 
tures. A third region of mechanical mixtures is indicated by the 
straight line representing the electrical conductivity between 38.4 
and 52 per cent, antimony. 

CHANGE OF THERMOELECTROMOTIVE FORCE WITH TEMPERATURE. 

The rate of variation of the thermoelectromotive force with 
the temperature for a large number of aluminium alloys has already 
been discussed. . The observations on these alloys were made by 
Broniewski. In his work the observations were extended over a 
limited range of temperature. The most important work in this 
connection is that of Giebel/^^ in which the observations were 
extended over a large range of temperature. He studied the fol- 
lowing series of alloys : Palladium-gold, palladium-platinum, palla- 
dium-silver, platinum-silver, platinum-rhodium, and platinum- 
iridium. The thermoelectromotive forces were measured against 
platinum in this case and the temperature of the cold junction was 
kept at 0° C. Observations were made at intervals of 100° C. 
between 0° and 900° C. The observed thermoelectromotive forces 
have been plotted against the temperatures in Figs. 52, 53 and 54. 
From Figs. 52 and 54 it is seen that the higher the temperature 
the more rapid is the rate of change of the thermoelectromotive 
force with the temperature for palladium-silver and for platinum- 
silver alloys. In the palladium-platinum series (Fig. 53) there is 
nearly a linear relation between the thermoelectromotive force and 
the temperature after the alloy contains about 40 per cent, platinum. 
When the concentration of platinum is increased above 40 per 
cent, this linear relation is more nearly realized. 

In Fig. 55 the thermoelectromotive force in platinum-rhodium 
alloy at a particular temperature has been plotted against the con- 
centration of rhodium in the alloy. These curves show that the 
thermoelectromotive force increases rapidly with the increase in 
the concentration of rhodium until the alloy contains about 5 per 
cent rhodium. Between 5 and 10 per cent, rhodium the increase 
is much less rapid, especially at low temperatures. Increasing the 

"^ Giebel : Zeit. anorg. Cheni., 69, 38, 1910, and 70, 240, 1911. 



74 



Alpheus W. Smith. 



[J. F. I. 



concentration of rhodium beyond lo per cent, changes only 
slightly the thermoelectromotive force until the temperature of the 
hot junction exceeds 1000° C. At very high temperatures the 
thermoelectromotive force continues to increase with increasing 
concentration of rhodium, but this rate of increase decreases with 
increasing concentration of rhodium. 

Fig. 52. 



Thermoelectric Forces of 
Platinum — Silver Alloys 
A gainst Plat in urn (t, = °C) 




200 100 600 

Temperature of Hot Junction °C 

The relation between the thermoelectromotive force and the 
difference in temperature between the junctions may be expressed 
by an equation of the form . 

E = at-^ht^-\-ct^ 

where one junction is kept at o° C. and the other at t° C. For a 
large number of metals and alloys it has been found that only the 
second power of the temperature need be considered. The equa- 
tion then becomes, to a very good approximation, 



Aug., 1921.] 



Properties of Alloys. 



75 



E = at-j-bt\ 
In such a case the rate of variation of the thermoelectromotive 
force with the temperature becomes 

4^ =P = a-\-2bt. 
a t 

This equation states that the thermoelectric power is a Hnear 

Fig. 53. 




200 400 600 800 1000 1200 
Temp, of Hot Junction °C 

function of the difference of temperature between the junctions. 
In some of the platinum-palladium alloys it has already been 
seen to be independent of the temperature. The rate of variation 
of the thermoelectric power with the temperature is 

dP , 

In so far as the approximation introduced above is correct the 
variation of the thermoelectric power with the temperature is the 
same for all temperatures. 



Alpheus W. Smith. 



LJ.F.I. 



THEORIES OF RESISTANCE AND THERMOELECTROMOTIVE FORCES. 

Lord Rayleigh ^'- and Liebenow/'" independent of each other, 
came to the conclusion that the increase in specific resistance which 

alloys show in excess of the resistance calculated from the resist- 

FiG. 54- 




200 300 400 500 6CC 100 SCO 900 
Temperature of Hot Junction T 

ance of their components may be attributed to the thermoelectro- 
motive forces which arise between the junctions of the metals 
forming the alloys. According to these theories, the electrical 
current passing from one layer of metal to another layer of the 
other metal in the alloy develops or absorbs heat at the surface of 
contact between the components of the alloy, on account of the 
Peltier eitect. These temperature diiterences cause thermoelectro- 
motive forces to be set up in the alloy in such a way that they are 
equivalent to a large number of small cells connected in series, so 
that they oppose the flow of the current through the substance. 
They have, therefore, the effect of an added resistance. Since the 
difference in temperature between the contacts is proportional to 
the current flowing in the conductor, and since the thermoelectro- 

"'" Lord Rayleigh: Xatiirc, 54, 154, 1896. 

^'^ Liebenow : Zeif. Electrochem., 4, 201 and 217. 



Aug., 1921. i 



Properties of Alloys. 



77 



motive forces are proportional to the difference in temperature, 
this back electromotive force is proportional to the current. The 
opposition to the flow of current through the alloy from this cause 
will, therefore, behave like a resistance and it will be impossible 
to distinguish between the ordinary resistance and that which 
arises from these thermoelectromotive forces. It is of importance 

Ftg. =;?. 



Thermoelectric Forces of 
Platium -Rhodium Alloys 

Against Platinum (t, = 0°C) 




Weight Per Cent. Rhodium 

to note that where the constituents form compounds in which the 
resistance is high, it is necessary on the basis of this theory to 
assume a thermoelectromotive force between the molecules. Such 
an assumption is not very probable. 

Some evidence for the correctness of this theory is found in 
the consideration of the way in which the electrical resistance of 
metals and alloys behaves at extremely low temperatures. When 
the temperature of a pure metal is decreased, the electrical resist- 
temperature, until the temperature is 3 or 4 degrees above the 
ance is found to be very accurately proportional to the absolute 



78 



Alpheus W. Smith. 



[J.F.L 



absolute zero where the superconducting state appears and the elec- 
trical resistance almost entirely disappears. If, on the other hand, 
the temperature of an impure metal or alloy is decreased indefi- 
nitely, the resistance does not disappear at the absolute zero, but 
approaches a constant value. This suggests that there is in the 
resistance of an alloy an added constant term which does not dis- 
appear at the absolute zero. The theory of Lord Rayleigh leads 
at once to the existence of such a term. The added resistance aris- 
ing from the causes considered in this theory does not seem large 
enough to account for the very high resistance of some alloys. 

Fig. 56. 



Rt 


Electrical Resistance 












Ho 
.060 

.055 

.050 
.045 
.040 
.035 
.030 
.025 
.020 
.015 


at Low Temperatures 
























/ 


















/ 
















/ 


/ 
















/ 


















V 
















V 






/ 










4^ 




/ 
















J>j- 


/ 










A 






M 

y PM 










/ 




r^ 


— V\o 
















^L^ 


— -^^^.^.^ 1 


.010 
.005 
000 






/ 








9S 




33,0^ 


i^-^^ 




y 


/ 




Li. 


i- 


^JJS.^ 







5 10 15 20 

Absolute Temperature — Degrees 

By reference to Fig. 56 it will be seen that the curve showing 
the relation between the electrical resistance of mercury and its 
temperature is nearly a straight line except near the origin. 
The curve for pure lead is also observed to be a straight line, but 
the corresponding curves for metals containing small admixtures 
of other metals do not seem to pass through the origin when pro- 
longed backward. In such cases the electrical resistance seems to 
approach a constant value which persists to the absolute zero. 
Such a constant value is to be expected on the basis of the theory 
proposed by Lord Rayleigh and may, therefore, be taken as par- 



Aug., 1921.] Properties of Alloys. 79 

tial evidence of the correctness of that theory. From the above 
point of view it is clear that it is impossible to prepare a good con- 
ductor by mixing two or more metals with each other. There will 
always be present this added resistance which makes the alloy at 
least not a better conductor than the constituents of which it is com- 
posed. Ordinarily the alloy is found to have a lower conductivity 
than would be calculated from its constituents by the additive law. 
This theory of Lord Rayleigh may be stated more fully 
as follows : 

Let Rq = the resistance of the alloy at 0° C. 

y = the temperature coefficient of resistance of the alloy. 

R = the resistance of the alloy at 0° C. calculated from its con- 
stituents by the additive law. 

Oj ^ the temperature coefficient of the alloy calculated by the addi- 
tive law. 

i?P = the contact resistance occurring at the surface of two metals 
forming the alloy. 

^ = the temperature coefficient of the constant resistance. 

Then, 

Roa + yt)=R(l-{-at)-{-R,a + ^t)- 
The resistance Re is, according to Lord Rayleigh and Liebe- 
now, caused by thermoelectromotive forces. 

Where it is possible to assume that the temperature coefficients 
y, a and ^ are independent of the temperature, it is possible 
to write, 

Ro = R-\- R^, and 0° C, 

and therefore, 

R^i = Ra + Rc^, 
at any temperature. 
Whence, 

Ra + Rcl^ 
'^= Ro • 

From this equation it is seen that 7 may be negative when ^ is 
negative and Re (S > R^. The temperature coefficient of alloys has 
been found negative in some cases. A well-known example is the 
case of copper-manganese alloys. Curves showing the ratio of the 
resistance at any temperature to the resistance at zero for some 



8o 



Alpheus W. Smith. 



[J. F. 1. 



copper-manganese alloys have been reproduced in Fig. 57. They 
are taken from the work of Guertler.^^* For an alloy containing 
12.3 per cent, of manganese the temperature coefficient is positive 
above and negative below 40° C. 



Rt 



1.006 



1.005 



1.004 



1.003 



1.002 



I.OOI 



1.000 



.999- 



FiG. 57. 



Copper -Manganese Alloys 






'1 


1 






/ 


/ 








1 


i 






/ 










I 


i 




/ 


? 












1 


/ 


/ 
















1 \ 
/ 








A, 


i^/?^ 


7 __._ 








^ 


t^ 


Mo / 


Qlo 


^^^^/° 


^ 


V 







-^ 


^ 


^ 

s 
















\ 


\ 























10 ZO 30 40 50 60 10 
Temperature °C 



90 100 



If it is possible to assume that /? = 0, that is, that the contact 
resistance is independent of the temperature, 



Guertler : Jahr. der Rad. und Elckt., 5, 17, i( 



Aug., I92I.] Properties of Alloys. 8i 

and since 



Ro 


= R+Rc, 


^or- 


=Ra 


Ro 

R '' 


a 



This equation is equivalent to the empirical rule stated by Matthies- 
sen and Vogt ; namely, that the observed temperature coefficient of 
the resistance divided by that calculated from the additive law is 
equal to the observed electrical conductivity divided by the elec- 
trical conductivity calculated from the additive law^. In so far as 
this rule may be accepted the curve for the electrical conductivity 
of a series of alloys ought to be the same as the curve for the 
temperature coefficient of that same series of alloys. In the pre- 
ceding pages it has been seen that in very many cases there is a 
parallelism betv^een the curve for the electrical conductivity and 
that for the temperature coefficient of the resistance. This parallel- 
ism offers satisfactory proof of the correctness of this rule in 
many cases. 

The theory of Lord Rayleigh also leads to the second rule 
stated by Matthiessen and Vogt. Since 

. R^{-^lyt)=^R{l^-at)-YRc, 
and 

R=R^R^^ 

Rg = Ro — jR = 

difference between observed and calculated resistance at o° C, and 

R, = Roa + yt)-Ra-\-(xt) = 

the difference between the observed and calculated resistance at 
t° C. Since each of these differences is equal to the contact 
resistance which has been assumed independent of the tempera- 
ture, these differences ought to be the same for all temperatures. 
In other words, the difference between the observed and the cal- 
culated resistance is the same whatever the temperature. The 
large number of cases in which this rule has been found to be 
verified gives evidence that the temperature coefficient of the 
contact resistance is either zero or very small. 

The increase in the electrical resistance of solid solutions over 
the resistance of the pure metals of which they are composed does 



82 Alpheus W. Smith. [J-F. I- 

not find an easy explanation on the basis of the electron theory of 
metallic conduction. One assumption which has been made to 
explain this increase is that the number of free electrons in the 
alloy is much less than in pure metals. This assumption when 
considered in connection with Wiedemann and Franz's law does 
not lead to satisfactory results. The departures from this law, 
which states that the ratio of the thermal to the electrical conduc- 
tivity is a constant for any particular temperature, are greater for 
alloys than for pure metals. These departures are always of such 
a nature that the electrical conductivity has been decreased more 
than the thermal conductivity by the formation of the alloy. This, 
with other considerations, has lead Schenck ^^^ to suggest that the 
increase in the electrical resistance of the alloy over the value cal- 
culated by the additive law could be accounted for by assuming 
that it arises from an increase in the frictional resistance which the 
electrons encounter in their motion through the alloy. This in- 
crease in frictional resistance to the motion of the electrons may be 
thought of as produced in a way very analogous to the way in 
which on the basis of the kinetic theory the addition of one gas 
to another causes an increase in the viscosity. Schenck thinks 
that the slowly diffusing molecules of the added metal hand on 
their energy and thus participate in the thermal conductivity but 
not in the process of electrical conduction. For this reason the 
ratio of the thermal to the electrical conductivity in mixed crystals 
is greater than for pure metals, and this quotient increases with 
increasing concentration of the added metal. The ratio of these 
CQnductivities in alloys as in pure metals is approximately propor- 
tional to the absolute temperature. 

According to the electron theory, the different concentration 
of the electrons in the two metals is the source of a diffusion 
current which is the cause of the thermoelectromotive force which 
arises when the junctions of two metals or alloys are at 
different temperatures. 

Let e = the thermoelectromotive force per degree difference in tem- 
perature. 
R = the gas constant in ergs. 
F = 965,450 coulombs. 
N(^ = number of electrons per cubic centimetre in A. 
Nj) = number of electrons per cubic centimetre in B. 

^'^ Schenck: Ann. d. Phys., 32, 261, 1910. 



Aug., 1921.] Properties of Alloys. 83 

Then, 

Many alloys give such large values of the thernioelectroniotive 
force against one of the pure metals of which they are composed 
that in the application of the above equation it is necessary to 
assume very large changes in the number of free electrons to be 
produced by adding one metal to the other. In order to avoid these 
improbable assumptions Schenck has introduced the assumption 
already referred to — that it is the friction of the free electrons 
rather than their number that is changed by alloying one metal 
with another. By using this assumption that there is an increase 
in the frictional resistance of the electrons in the alloys over the 
resistance which they experience in pure metals, Schenck has been 
able to derive a relation between the thermal and electrical con- 
ductivity of the alloy, the thermal and electrical conductivity of the 
pure metallic solvent, and the thermoelectric power of the alloy 
against the pure solvent. 

Let k = thermal conductivity of the pure solvent. 

a — electrical conductivity of the pure solvent. 

k' = the thermal conductivity of the alloy. 

0-' = the electrical conductivity of the alloy. 

TT = the thermo-electromotive force of the solid solution against the 
pure solvent for 1° C. temperature difference between the 
junctions. 

R = the gas constant. 

e ■= the specific electrical charge = 96,540 coulombs. 

Then for dilute solutions Schenck shows that 

Some observations have been made by Bernoulli ^^^ to test the 
validity of this equation. The following table shows the kind of 
agreement which exists between the observed and calculated values. 

''" Bernoulli : Ann. d. Phys., 33, 690, 1910. 



84 



Alpheus W. Smith. 



[J.F.I. 



Solrent. 


Element in solution. 


TT 

Observed. 


TT 

Calculated. 


Silver . ... 


2.73 percent. Th. 
4.76 per cent. Th. 
4.00 per cent. Sn. 

5.14 per cent. Hg. 
1 0.0 percent. Hg. 

5.00 percent. Sn. 
3.1 1 percent. Zn. 
5.00 per cent. Zn. 
3.94 per cent, Ni. 
17.30 percent. Ni. 


2.8 

10.3 

7.6 

2.8 
2.6 

3.4 
2.9 
1.4 

13-3 
27-3 


2.6 


Cadmium 


8.4 
8.9 

2.2 


Copper 


3.0 
3.6 

3.9 
II.2 





From this table it is seen that for dilute solutions fair agree- 
ment exists between the observed and the calculated values. The 
more concentrated the solution the less satisfactory is the agreement. 



RESISTANCE AKD HARDNESS. 

A theory of electrical conductivity proposed by March ^^^ 
offers a possible explanation of the relation between the elastic 
properties and the electrical conductivity of alloys. According to 
this theory, the number of free electrons in a metal or alloy, and 
therefore the electrical conductivity, is in part, at least, determined 
by the characteristic frequency of vibration of the atoms about 
their positions of equilibrium. Whatever changes this character- 
istic frequency would change at the same time the elastic prop- 
erties and the thermal and electrical properties. On the basis of 
this theory the number of free electrons decrease with increasing 
frequency of the characteristic vibration of the atoms. Whatever, 
therefore, decreases the frequency of the characteristic vibrations 
of the atoms increases the electrical conductivity of the substance. 
Hence, at the absolute zero where the characteristic frequency of 
vibration of the atoms is very small or else disappears, the elec- 
trical conductivity will be very large. This is, of course, exactly 
wliat is observed in metals at very low temperatures where they 
pass into the superconducting state. 

The formation of a solid solution produces a change in the 
elastic properties which causes the characteristic frequency of 
vibration of the atoms to increase. This arises out of the fact 

^"^ March : Ann. d. Phys., 49, 710, 191 6. 



Aug., 1921.] Properties of Alloys. 85 

that in an alloy in which the components A and B form mixed 
crystals, a molecule of A and a molecule of B act on each other 
with greater force than that with which a molecule of ^ acts on a 
molecule oi A or a molecule of ^ on a molecule oi B. There is on 
this account an increase in the cohesive forces and consequently 
an increase in the characteristic frequency of vibration of the 
atoms. With this increase in frequency is associated a decrease in 
the number of free electrons and a corresponding increase in the 
electrical resistance. From this point of view it is possible to see 
that where such elastic properties as hardness or tensile strength 
have maximum values, the electrical resistance will have a maxi- 
mum value and the electrical conductivity a minimum value. Many 
illustrations of this have been seen in the preceding curves. 

If the two components A and B oi the alloy are insoluble in 
each other, the force which the molecule A exerts on another 
molecule A or the force which a molecule B exerts on another 
molecule B exceeds the force which a molecule A exerts on a mole- 
cule B or that which a molecule B exerts on a molecule A. Con- 
sequently each of these classes of molecules will form a group of 
crystals and the alloy will be a conglomerate formed of groups 
of crystals of the two constituents. In such an alloy the character- 
istics of each constituent are retained and the physical properties are 
additive. The components will, therefore, retain their character- 
istic vibrations and their elastic properties as well as the number 
of free electrons, and the electrical conductivity will change in 
conformity to the additive law. The hardness which increases 
with the frequency of the characteristic vibration of the atoms 
should in such cases be a linear function of the concentration of 
one of the constituents in the alloy. In such alloys the electrical 
conductivity will also be a linear function of the concentration of 
one of the constituents. Many cases of this kind have been noted 
in the preceding pages. This theory seems to offer a possible ex- 
planation of some of the interesting relations noted among the 
physical properties of alloys. Although the theory may not be sat- 
isfactory in many particulars, it is without doubt very suggestive. 

Grateful acknowledgment is made to the Engineering Experi- 
ment Station of the Ohio State University for generous financial 
assistance in aid of this work. 

Physical Laboratory, 

Ohio State University. 



